Lecture Notes For MATH305
Lecture Notes Lecture Notes 1-Notes on Fundamentals (Sections 1.1-1.6, 2.1) Extra Notes
Lecture Notes Lecture Notes 2-Notes on Analyticity (Sections 2.2--2.5) Proof of Theorem 2 on CR Equations (expanded version: page 75 of book)
Lecture Notes 2.5 Lecture Notes on Conformal Mappings and Laplace Equation
Lecture Notes 3 Lecture Notes 3- Notes on Some Simple Functions (Sections 3.1-3.2)
Lecture Notes 4 Lecture Notes 4-Notes on Multi-valued Functions (Sections 3.3 and 3.5) (Also take a look at these notes on branch cuts by Prof. Rosales of MIT) (Here are also a few additional carefully worked out problems with branch cuts)
Lecture Notes 4.5 Lecture Notes 4.5-Notes on inverse function of sin (z)
Lecture Notes 5 Lecture Notes 5-Notes on Contour Integration, Cauchy's Integral Theorem (Sections 4.1--4.3): First batch of notes Second batch of notes
Lecture Notes 6 Lecture Notes 6-Notes on Nyquist Criterion
Lecture Notes 6.5 Lecture Notes 6.5-Notes on Rouche's Theorem
Lecture Notes 7 Lecture Notes 7-Notes on Residue Calculus
Lecture Notes 8 Lecture Notes 8-Notes on Integration by Residue Calculus
Lecture Notes 8-5 Lecture Notes 8-5: A Summary
Lecture Notes 9 Lecture Notes 9- Notes on Laurent Series, Singularities and Residue Calculus
Lecture Notes 10 Lecture Notes 10- Notes on Fourier Transforms and Applications
Downloads For MATH305
Download 1: Syllabus
Download 2: HW1 (Due Date: Jan. 13, by 5:30pm)
Download 3: Solutions to HW1
Download 4: HW2 (Due Date: Jan. 23, by 5:30pm)
Download 5: HW3 (Due Date: Jan. 30, by 5:30pm)
Download 6: Solutions to HW2
Download 7: HW4 (Due Date: Feb. 6, by 5:30pm)
Download 8: Solutions to HW3
Download 9: Past Midterm 1-1
Download 10: Past Midterm 1-2
Download 11: Past Midterm 1-3
Download 12: HW5 (Due Date: Feb. 15, by 5:30pm)
Download 13: Solutions to HW4
Download 14: Midterm One and Solutions
Download 15: Solutions to HW5
Download 16: HW6 (Due: Feb. 27)
Download 17: Solutions to HW6
Download 18: HW7 (Due: March 6)
Download 19: Solutions to HW7
Download 20: HW8 (Due: March 13)
Download 21: Solutions to HW8
Download 22: HW9 (Due: March 22)
Download 23: Past Midterm 2-1
Download 24: Past Midterm 2-2
Download 25: Past Midterm 2-3
Download 26: Past Sample Problems
Download 27: Solutions to HW9
Download 28: Solutions to Midterm Examination 2
Download 29: HW10 (Due: April 7)
Download 30: Solutions to HW10
Download 31: Past Review Problems
Download 32: Solutions to Past Review Problems
Download 33: Past Final Exam
Updates For MATH 305
Jan. 4: Fundamentals of complex variable. Euler's formula. Polar coordinate. Principal value of argument Arg (z).
Jan. 6: Arg (z) and arg (z). De Moivre's formula. Roots of unit. Roots of a complex variable.
Jan. 9: Complex exponential. Sets in the complex plane. Functions of complex variables.
Jan. 11: Functions of complex variables. Image under linear and Mobius map $ w=(a+bz)/ (c+dz)$.
Jan. 13: Image under $w=z^2$. Continuous, differentiable, analytic. Cauchy-Riemann equation.
Jan. 16: Consequences of Cauchy-Riemann equation. Harmonic Functions. Conformal Mapping. Level Sets. More notes can be found here. Lecture Notes on Conformal Mappings
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Lecture Notes Lecture Notes 2-Notes on Analyticity (Sections 2.2--2.5) Proof of Theorem 2 on CR Equations (expanded version: page 75 of book)
Lecture Notes 2.5 Lecture Notes on Conformal Mappings and Laplace Equation
Lecture Notes 3 Lecture Notes 3- Notes on Some Simple Functions (Sections 3.1-3.2)
Lecture Notes 4 Lecture Notes 4-Notes on Multi-valued Functions (Sections 3.3 and 3.5) (Also take a look at these notes on branch cuts by Prof. Rosales of MIT) (Here are also a few additional carefully worked out problems with branch cuts)
Lecture Notes 4.5 Lecture Notes 4.5-Notes on inverse function of sin (z)
Lecture Notes 5 Lecture Notes 5-Notes on Contour Integration, Cauchy's Integral Theorem (Sections 4.1--4.3): First batch of notes Second batch of notes
Lecture Notes 6 Lecture Notes 6-Notes on Nyquist Criterion
Lecture Notes 6.5 Lecture Notes 6.5-Notes on Rouche's Theorem
Lecture Notes 7 Lecture Notes 7-Notes on Residue Calculus
Lecture Notes 8 Lecture Notes 8-Notes on Integration by Residue Calculus
Lecture Notes 8-5 Lecture Notes 8-5: A Summary
Lecture Notes 9 Lecture Notes 9- Notes on Laurent Series, Singularities and Residue Calculus
Lecture Notes 10 Lecture Notes 10- Notes on Fourier Transforms and Applications
Downloads For MATH305
Download 1: Syllabus
Download 2: HW1 (Due Date: Jan. 13, by 5:30pm)
Download 3: Solutions to HW1
Download 4: HW2 (Due Date: Jan. 23, by 5:30pm)
Download 5: HW3 (Due Date: Jan. 30, by 5:30pm)
Download 6: Solutions to HW2
Download 7: HW4 (Due Date: Feb. 6, by 5:30pm)
Download 8: Solutions to HW3
Download 9: Past Midterm 1-1
Download 10: Past Midterm 1-2
Download 11: Past Midterm 1-3
Download 12: HW5 (Due Date: Feb. 15, by 5:30pm)
Download 13: Solutions to HW4
Download 14: Midterm One and Solutions
Download 15: Solutions to HW5
Download 16: HW6 (Due: Feb. 27)
Download 17: Solutions to HW6
Download 18: HW7 (Due: March 6)
Download 19: Solutions to HW7
Download 20: HW8 (Due: March 13)
Download 21: Solutions to HW8
Download 22: HW9 (Due: March 22)
Download 23: Past Midterm 2-1
Download 24: Past Midterm 2-2
Download 25: Past Midterm 2-3
Download 26: Past Sample Problems
Download 27: Solutions to HW9
Download 28: Solutions to Midterm Examination 2
Download 29: HW10 (Due: April 7)
Download 30: Solutions to HW10
Download 31: Past Review Problems
Download 32: Solutions to Past Review Problems
Download 33: Past Final Exam
Updates For MATH 305
Jan. 4: Fundamentals of complex variable. Euler's formula. Polar coordinate. Principal value of argument Arg (z).
Jan. 6: Arg (z) and arg (z). De Moivre's formula. Roots of unit. Roots of a complex variable.
Jan. 9: Complex exponential. Sets in the complex plane. Functions of complex variables.
Jan. 11: Functions of complex variables. Image under linear and Mobius map $ w=(a+bz)/ (c+dz)$.
Jan. 13: Image under $w=z^2$. Continuous, differentiable, analytic. Cauchy-Riemann equation.
Jan. 16: Consequences of Cauchy-Riemann equation. Harmonic Functions. Conformal Mapping. Level Sets. More notes can be found here. Lecture Notes on Conformal Mappings
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Lecture Notes 2.5 Lecture Notes on Conformal Mappings and Laplace Equation
Lecture Notes 3 Lecture Notes 3- Notes on Some Simple Functions (Sections 3.1-3.2)
Lecture Notes 4 Lecture Notes 4-Notes on Multi-valued Functions (Sections 3.3 and 3.5) (Also take a look at these notes on branch cuts by Prof. Rosales of MIT) (Here are also a few additional carefully worked out problems with branch cuts)
Lecture Notes 4.5 Lecture Notes 4.5-Notes on inverse function of sin (z)
Lecture Notes 5 Lecture Notes 5-Notes on Contour Integration, Cauchy's Integral Theorem (Sections 4.1--4.3): First batch of notes Second batch of notes
Lecture Notes 6 Lecture Notes 6-Notes on Nyquist Criterion
Lecture Notes 6.5 Lecture Notes 6.5-Notes on Rouche's Theorem
Lecture Notes 7 Lecture Notes 7-Notes on Residue Calculus
Lecture Notes 8 Lecture Notes 8-Notes on Integration by Residue Calculus
Lecture Notes 8-5 Lecture Notes 8-5: A Summary
Lecture Notes 9 Lecture Notes 9- Notes on Laurent Series, Singularities and Residue Calculus
Lecture Notes 10 Lecture Notes 10- Notes on Fourier Transforms and Applications
Downloads For MATH305
Download 1: Syllabus
Download 2: HW1 (Due Date: Jan. 13, by 5:30pm)
Download 3: Solutions to HW1
Download 4: HW2 (Due Date: Jan. 23, by 5:30pm)
Download 5: HW3 (Due Date: Jan. 30, by 5:30pm)
Download 6: Solutions to HW2
Download 7: HW4 (Due Date: Feb. 6, by 5:30pm)
Download 8: Solutions to HW3
Download 9: Past Midterm 1-1
Download 10: Past Midterm 1-2
Download 11: Past Midterm 1-3
Download 12: HW5 (Due Date: Feb. 15, by 5:30pm)
Download 13: Solutions to HW4
Download 14: Midterm One and Solutions
Download 15: Solutions to HW5
Download 16: HW6 (Due: Feb. 27)
Download 17: Solutions to HW6
Download 18: HW7 (Due: March 6)
Download 19: Solutions to HW7
Download 20: HW8 (Due: March 13)
Download 21: Solutions to HW8
Download 22: HW9 (Due: March 22)
Download 23: Past Midterm 2-1
Download 24: Past Midterm 2-2
Download 25: Past Midterm 2-3
Download 26: Past Sample Problems
Download 27: Solutions to HW9
Download 28: Solutions to Midterm Examination 2
Download 29: HW10 (Due: April 7)
Download 30: Solutions to HW10
Download 31: Past Review Problems
Download 32: Solutions to Past Review Problems
Download 33: Past Final Exam
Updates For MATH 305
Jan. 4: Fundamentals of complex variable. Euler's formula. Polar coordinate. Principal value of argument Arg (z).
Jan. 6: Arg (z) and arg (z). De Moivre's formula. Roots of unit. Roots of a complex variable.
Jan. 9: Complex exponential. Sets in the complex plane. Functions of complex variables.
Jan. 11: Functions of complex variables. Image under linear and Mobius map $ w=(a+bz)/ (c+dz)$.
Jan. 13: Image under $w=z^2$. Continuous, differentiable, analytic. Cauchy-Riemann equation.
Jan. 16: Consequences of Cauchy-Riemann equation. Harmonic Functions. Conformal Mapping. Level Sets. More notes can be found here. Lecture Notes on Conformal Mappings
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Lecture Notes 3 Lecture Notes 3- Notes on Some Simple Functions (Sections 3.1-3.2)
Lecture Notes 4 Lecture Notes 4-Notes on Multi-valued Functions (Sections 3.3 and 3.5) (Also take a look at these notes on branch cuts by Prof. Rosales of MIT) (Here are also a few additional carefully worked out problems with branch cuts)
Lecture Notes 4.5 Lecture Notes 4.5-Notes on inverse function of sin (z)
Lecture Notes 5 Lecture Notes 5-Notes on Contour Integration, Cauchy's Integral Theorem (Sections 4.1--4.3): First batch of notes Second batch of notes
Lecture Notes 6 Lecture Notes 6-Notes on Nyquist Criterion
Lecture Notes 6.5 Lecture Notes 6.5-Notes on Rouche's Theorem
Lecture Notes 7 Lecture Notes 7-Notes on Residue Calculus
Lecture Notes 8 Lecture Notes 8-Notes on Integration by Residue Calculus
Lecture Notes 8-5 Lecture Notes 8-5: A Summary
Lecture Notes 9 Lecture Notes 9- Notes on Laurent Series, Singularities and Residue Calculus
Lecture Notes 10 Lecture Notes 10- Notes on Fourier Transforms and Applications
Downloads For MATH305
Download 1: Syllabus
Download 2: HW1 (Due Date: Jan. 13, by 5:30pm)
Download 3: Solutions to HW1
Download 4: HW2 (Due Date: Jan. 23, by 5:30pm)
Download 5: HW3 (Due Date: Jan. 30, by 5:30pm)
Download 6: Solutions to HW2
Download 7: HW4 (Due Date: Feb. 6, by 5:30pm)
Download 8: Solutions to HW3
Download 9: Past Midterm 1-1
Download 10: Past Midterm 1-2
Download 11: Past Midterm 1-3
Download 12: HW5 (Due Date: Feb. 15, by 5:30pm)
Download 13: Solutions to HW4
Download 14: Midterm One and Solutions
Download 15: Solutions to HW5
Download 16: HW6 (Due: Feb. 27)
Download 17: Solutions to HW6
Download 18: HW7 (Due: March 6)
Download 19: Solutions to HW7
Download 20: HW8 (Due: March 13)
Download 21: Solutions to HW8
Download 22: HW9 (Due: March 22)
Download 23: Past Midterm 2-1
Download 24: Past Midterm 2-2
Download 25: Past Midterm 2-3
Download 26: Past Sample Problems
Download 27: Solutions to HW9
Download 28: Solutions to Midterm Examination 2
Download 29: HW10 (Due: April 7)
Download 30: Solutions to HW10
Download 31: Past Review Problems
Download 32: Solutions to Past Review Problems
Download 33: Past Final Exam
Updates For MATH 305
Jan. 4: Fundamentals of complex variable. Euler's formula. Polar coordinate. Principal value of argument Arg (z).
Jan. 6: Arg (z) and arg (z). De Moivre's formula. Roots of unit. Roots of a complex variable.
Jan. 9: Complex exponential. Sets in the complex plane. Functions of complex variables.
Jan. 11: Functions of complex variables. Image under linear and Mobius map $ w=(a+bz)/ (c+dz)$.
Jan. 13: Image under $w=z^2$. Continuous, differentiable, analytic. Cauchy-Riemann equation.
Jan. 16: Consequences of Cauchy-Riemann equation. Harmonic Functions. Conformal Mapping. Level Sets. More notes can be found here. Lecture Notes on Conformal Mappings
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Lecture Notes 4 Lecture Notes 4-Notes on Multi-valued Functions (Sections 3.3 and 3.5) (Also take a look at these notes on branch cuts by Prof. Rosales of MIT) (Here are also a few additional carefully worked out problems with branch cuts)
Lecture Notes 4.5 Lecture Notes 4.5-Notes on inverse function of sin (z)
Lecture Notes 5 Lecture Notes 5-Notes on Contour Integration, Cauchy's Integral Theorem (Sections 4.1--4.3): First batch of notes Second batch of notes
Lecture Notes 6 Lecture Notes 6-Notes on Nyquist Criterion
Lecture Notes 6.5 Lecture Notes 6.5-Notes on Rouche's Theorem
Lecture Notes 7 Lecture Notes 7-Notes on Residue Calculus
Lecture Notes 8 Lecture Notes 8-Notes on Integration by Residue Calculus
Lecture Notes 8-5 Lecture Notes 8-5: A Summary
Lecture Notes 9 Lecture Notes 9- Notes on Laurent Series, Singularities and Residue Calculus
Lecture Notes 10 Lecture Notes 10- Notes on Fourier Transforms and Applications
Downloads For MATH305
Download 1: Syllabus
Download 2: HW1 (Due Date: Jan. 13, by 5:30pm)
Download 3: Solutions to HW1
Download 4: HW2 (Due Date: Jan. 23, by 5:30pm)
Download 5: HW3 (Due Date: Jan. 30, by 5:30pm)
Download 6: Solutions to HW2
Download 7: HW4 (Due Date: Feb. 6, by 5:30pm)
Download 8: Solutions to HW3
Download 9: Past Midterm 1-1
Download 10: Past Midterm 1-2
Download 11: Past Midterm 1-3
Download 12: HW5 (Due Date: Feb. 15, by 5:30pm)
Download 13: Solutions to HW4
Download 14: Midterm One and Solutions
Download 15: Solutions to HW5
Download 16: HW6 (Due: Feb. 27)
Download 17: Solutions to HW6
Download 18: HW7 (Due: March 6)
Download 19: Solutions to HW7
Download 20: HW8 (Due: March 13)
Download 21: Solutions to HW8
Download 22: HW9 (Due: March 22)
Download 23: Past Midterm 2-1
Download 24: Past Midterm 2-2
Download 25: Past Midterm 2-3
Download 26: Past Sample Problems
Download 27: Solutions to HW9
Download 28: Solutions to Midterm Examination 2
Download 29: HW10 (Due: April 7)
Download 30: Solutions to HW10
Download 31: Past Review Problems
Download 32: Solutions to Past Review Problems
Download 33: Past Final Exam
Updates For MATH 305
Jan. 4: Fundamentals of complex variable. Euler's formula. Polar coordinate. Principal value of argument Arg (z).
Jan. 6: Arg (z) and arg (z). De Moivre's formula. Roots of unit. Roots of a complex variable.
Jan. 9: Complex exponential. Sets in the complex plane. Functions of complex variables.
Jan. 11: Functions of complex variables. Image under linear and Mobius map $ w=(a+bz)/ (c+dz)$.
Jan. 13: Image under $w=z^2$. Continuous, differentiable, analytic. Cauchy-Riemann equation.
Jan. 16: Consequences of Cauchy-Riemann equation. Harmonic Functions. Conformal Mapping. Level Sets. More notes can be found here. Lecture Notes on Conformal Mappings
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Lecture Notes 4.5 Lecture Notes 4.5-Notes on inverse function of sin (z)
Lecture Notes 5 Lecture Notes 5-Notes on Contour Integration, Cauchy's Integral Theorem (Sections 4.1--4.3): First batch of notes Second batch of notes
Lecture Notes 6 Lecture Notes 6-Notes on Nyquist Criterion
Lecture Notes 6.5 Lecture Notes 6.5-Notes on Rouche's Theorem
Lecture Notes 7 Lecture Notes 7-Notes on Residue Calculus
Lecture Notes 8 Lecture Notes 8-Notes on Integration by Residue Calculus
Lecture Notes 8-5 Lecture Notes 8-5: A Summary
Lecture Notes 9 Lecture Notes 9- Notes on Laurent Series, Singularities and Residue Calculus
Lecture Notes 10 Lecture Notes 10- Notes on Fourier Transforms and Applications
Downloads For MATH305
Download 1: Syllabus
Download 2: HW1 (Due Date: Jan. 13, by 5:30pm)
Download 3: Solutions to HW1
Download 4: HW2 (Due Date: Jan. 23, by 5:30pm)
Download 5: HW3 (Due Date: Jan. 30, by 5:30pm)
Download 6: Solutions to HW2
Download 7: HW4 (Due Date: Feb. 6, by 5:30pm)
Download 8: Solutions to HW3
Download 9: Past Midterm 1-1
Download 10: Past Midterm 1-2
Download 11: Past Midterm 1-3
Download 12: HW5 (Due Date: Feb. 15, by 5:30pm)
Download 13: Solutions to HW4
Download 14: Midterm One and Solutions
Download 15: Solutions to HW5
Download 16: HW6 (Due: Feb. 27)
Download 17: Solutions to HW6
Download 18: HW7 (Due: March 6)
Download 19: Solutions to HW7
Download 20: HW8 (Due: March 13)
Download 21: Solutions to HW8
Download 22: HW9 (Due: March 22)
Download 23: Past Midterm 2-1
Download 24: Past Midterm 2-2
Download 25: Past Midterm 2-3
Download 26: Past Sample Problems
Download 27: Solutions to HW9
Download 28: Solutions to Midterm Examination 2
Download 29: HW10 (Due: April 7)
Download 30: Solutions to HW10
Download 31: Past Review Problems
Download 32: Solutions to Past Review Problems
Download 33: Past Final Exam
Updates For MATH 305
Jan. 4: Fundamentals of complex variable. Euler's formula. Polar coordinate. Principal value of argument Arg (z).
Jan. 6: Arg (z) and arg (z). De Moivre's formula. Roots of unit. Roots of a complex variable.
Jan. 9: Complex exponential. Sets in the complex plane. Functions of complex variables.
Jan. 11: Functions of complex variables. Image under linear and Mobius map $ w=(a+bz)/ (c+dz)$.
Jan. 13: Image under $w=z^2$. Continuous, differentiable, analytic. Cauchy-Riemann equation.
Jan. 16: Consequences of Cauchy-Riemann equation. Harmonic Functions. Conformal Mapping. Level Sets. More notes can be found here. Lecture Notes on Conformal Mappings
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Lecture Notes 5 Lecture Notes 5-Notes on Contour Integration, Cauchy's Integral Theorem (Sections 4.1--4.3): First batch of notes Second batch of notes
Lecture Notes 6 Lecture Notes 6-Notes on Nyquist Criterion
Lecture Notes 6.5 Lecture Notes 6.5-Notes on Rouche's Theorem
Lecture Notes 7 Lecture Notes 7-Notes on Residue Calculus
Lecture Notes 8 Lecture Notes 8-Notes on Integration by Residue Calculus
Lecture Notes 8-5 Lecture Notes 8-5: A Summary
Lecture Notes 9 Lecture Notes 9- Notes on Laurent Series, Singularities and Residue Calculus
Lecture Notes 10 Lecture Notes 10- Notes on Fourier Transforms and Applications
Downloads For MATH305
Download 1: Syllabus
Download 2: HW1 (Due Date: Jan. 13, by 5:30pm)
Download 3: Solutions to HW1
Download 4: HW2 (Due Date: Jan. 23, by 5:30pm)
Download 5: HW3 (Due Date: Jan. 30, by 5:30pm)
Download 6: Solutions to HW2
Download 7: HW4 (Due Date: Feb. 6, by 5:30pm)
Download 8: Solutions to HW3
Download 9: Past Midterm 1-1
Download 10: Past Midterm 1-2
Download 11: Past Midterm 1-3
Download 12: HW5 (Due Date: Feb. 15, by 5:30pm)
Download 13: Solutions to HW4
Download 14: Midterm One and Solutions
Download 15: Solutions to HW5
Download 16: HW6 (Due: Feb. 27)
Download 17: Solutions to HW6
Download 18: HW7 (Due: March 6)
Download 19: Solutions to HW7
Download 20: HW8 (Due: March 13)
Download 21: Solutions to HW8
Download 22: HW9 (Due: March 22)
Download 23: Past Midterm 2-1
Download 24: Past Midterm 2-2
Download 25: Past Midterm 2-3
Download 26: Past Sample Problems
Download 27: Solutions to HW9
Download 28: Solutions to Midterm Examination 2
Download 29: HW10 (Due: April 7)
Download 30: Solutions to HW10
Download 31: Past Review Problems
Download 32: Solutions to Past Review Problems
Download 33: Past Final Exam
Updates For MATH 305
Jan. 4: Fundamentals of complex variable. Euler's formula. Polar coordinate. Principal value of argument Arg (z).
Jan. 6: Arg (z) and arg (z). De Moivre's formula. Roots of unit. Roots of a complex variable.
Jan. 9: Complex exponential. Sets in the complex plane. Functions of complex variables.
Jan. 11: Functions of complex variables. Image under linear and Mobius map $ w=(a+bz)/ (c+dz)$.
Jan. 13: Image under $w=z^2$. Continuous, differentiable, analytic. Cauchy-Riemann equation.
Jan. 16: Consequences of Cauchy-Riemann equation. Harmonic Functions. Conformal Mapping. Level Sets. More notes can be found here. Lecture Notes on Conformal Mappings
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Lecture Notes 6 Lecture Notes 6-Notes on Nyquist Criterion
Lecture Notes 6.5 Lecture Notes 6.5-Notes on Rouche's Theorem
Lecture Notes 7 Lecture Notes 7-Notes on Residue Calculus
Lecture Notes 8 Lecture Notes 8-Notes on Integration by Residue Calculus
Lecture Notes 8-5 Lecture Notes 8-5: A Summary
Lecture Notes 9 Lecture Notes 9- Notes on Laurent Series, Singularities and Residue Calculus
Lecture Notes 10 Lecture Notes 10- Notes on Fourier Transforms and Applications
Downloads For MATH305
Download 1: Syllabus
Download 2: HW1 (Due Date: Jan. 13, by 5:30pm)
Download 3: Solutions to HW1
Download 4: HW2 (Due Date: Jan. 23, by 5:30pm)
Download 5: HW3 (Due Date: Jan. 30, by 5:30pm)
Download 6: Solutions to HW2
Download 7: HW4 (Due Date: Feb. 6, by 5:30pm)
Download 8: Solutions to HW3
Download 9: Past Midterm 1-1
Download 10: Past Midterm 1-2
Download 11: Past Midterm 1-3
Download 12: HW5 (Due Date: Feb. 15, by 5:30pm)
Download 13: Solutions to HW4
Download 14: Midterm One and Solutions
Download 15: Solutions to HW5
Download 16: HW6 (Due: Feb. 27)
Download 17: Solutions to HW6
Download 18: HW7 (Due: March 6)
Download 19: Solutions to HW7
Download 20: HW8 (Due: March 13)
Download 21: Solutions to HW8
Download 22: HW9 (Due: March 22)
Download 23: Past Midterm 2-1
Download 24: Past Midterm 2-2
Download 25: Past Midterm 2-3
Download 26: Past Sample Problems
Download 27: Solutions to HW9
Download 28: Solutions to Midterm Examination 2
Download 29: HW10 (Due: April 7)
Download 30: Solutions to HW10
Download 31: Past Review Problems
Download 32: Solutions to Past Review Problems
Download 33: Past Final Exam
Updates For MATH 305
Jan. 4: Fundamentals of complex variable. Euler's formula. Polar coordinate. Principal value of argument Arg (z).
Jan. 6: Arg (z) and arg (z). De Moivre's formula. Roots of unit. Roots of a complex variable.
Jan. 9: Complex exponential. Sets in the complex plane. Functions of complex variables.
Jan. 11: Functions of complex variables. Image under linear and Mobius map $ w=(a+bz)/ (c+dz)$.
Jan. 13: Image under $w=z^2$. Continuous, differentiable, analytic. Cauchy-Riemann equation.
Jan. 16: Consequences of Cauchy-Riemann equation. Harmonic Functions. Conformal Mapping. Level Sets. More notes can be found here. Lecture Notes on Conformal Mappings
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Lecture Notes 6.5 Lecture Notes 6.5-Notes on Rouche's Theorem
Lecture Notes 7 Lecture Notes 7-Notes on Residue Calculus
Lecture Notes 8 Lecture Notes 8-Notes on Integration by Residue Calculus
Lecture Notes 8-5 Lecture Notes 8-5: A Summary
Lecture Notes 9 Lecture Notes 9- Notes on Laurent Series, Singularities and Residue Calculus
Lecture Notes 10 Lecture Notes 10- Notes on Fourier Transforms and Applications
Downloads For MATH305
Download 1: Syllabus
Download 2: HW1 (Due Date: Jan. 13, by 5:30pm)
Download 3: Solutions to HW1
Download 4: HW2 (Due Date: Jan. 23, by 5:30pm)
Download 5: HW3 (Due Date: Jan. 30, by 5:30pm)
Download 6: Solutions to HW2
Download 7: HW4 (Due Date: Feb. 6, by 5:30pm)
Download 8: Solutions to HW3
Download 9: Past Midterm 1-1
Download 10: Past Midterm 1-2
Download 11: Past Midterm 1-3
Download 12: HW5 (Due Date: Feb. 15, by 5:30pm)
Download 13: Solutions to HW4
Download 14: Midterm One and Solutions
Download 15: Solutions to HW5
Download 16: HW6 (Due: Feb. 27)
Download 17: Solutions to HW6
Download 18: HW7 (Due: March 6)
Download 19: Solutions to HW7
Download 20: HW8 (Due: March 13)
Download 21: Solutions to HW8
Download 22: HW9 (Due: March 22)
Download 23: Past Midterm 2-1
Download 24: Past Midterm 2-2
Download 25: Past Midterm 2-3
Download 26: Past Sample Problems
Download 27: Solutions to HW9
Download 28: Solutions to Midterm Examination 2
Download 29: HW10 (Due: April 7)
Download 30: Solutions to HW10
Download 31: Past Review Problems
Download 32: Solutions to Past Review Problems
Download 33: Past Final Exam
Updates For MATH 305
Jan. 4: Fundamentals of complex variable. Euler's formula. Polar coordinate. Principal value of argument Arg (z).
Jan. 6: Arg (z) and arg (z). De Moivre's formula. Roots of unit. Roots of a complex variable.
Jan. 9: Complex exponential. Sets in the complex plane. Functions of complex variables.
Jan. 11: Functions of complex variables. Image under linear and Mobius map $ w=(a+bz)/ (c+dz)$.
Jan. 13: Image under $w=z^2$. Continuous, differentiable, analytic. Cauchy-Riemann equation.
Jan. 16: Consequences of Cauchy-Riemann equation. Harmonic Functions. Conformal Mapping. Level Sets. More notes can be found here. Lecture Notes on Conformal Mappings
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Lecture Notes 7 Lecture Notes 7-Notes on Residue Calculus
Lecture Notes 8 Lecture Notes 8-Notes on Integration by Residue Calculus
Lecture Notes 8-5 Lecture Notes 8-5: A Summary
Lecture Notes 9 Lecture Notes 9- Notes on Laurent Series, Singularities and Residue Calculus
Lecture Notes 10 Lecture Notes 10- Notes on Fourier Transforms and Applications
Downloads For MATH305
Download 1: Syllabus
Download 2: HW1 (Due Date: Jan. 13, by 5:30pm)
Download 3: Solutions to HW1
Download 4: HW2 (Due Date: Jan. 23, by 5:30pm)
Download 5: HW3 (Due Date: Jan. 30, by 5:30pm)
Download 6: Solutions to HW2
Download 7: HW4 (Due Date: Feb. 6, by 5:30pm)
Download 8: Solutions to HW3
Download 9: Past Midterm 1-1
Download 10: Past Midterm 1-2
Download 11: Past Midterm 1-3
Download 12: HW5 (Due Date: Feb. 15, by 5:30pm)
Download 13: Solutions to HW4
Download 14: Midterm One and Solutions
Download 15: Solutions to HW5
Download 16: HW6 (Due: Feb. 27)
Download 17: Solutions to HW6
Download 18: HW7 (Due: March 6)
Download 19: Solutions to HW7
Download 20: HW8 (Due: March 13)
Download 21: Solutions to HW8
Download 22: HW9 (Due: March 22)
Download 23: Past Midterm 2-1
Download 24: Past Midterm 2-2
Download 25: Past Midterm 2-3
Download 26: Past Sample Problems
Download 27: Solutions to HW9
Download 28: Solutions to Midterm Examination 2
Download 29: HW10 (Due: April 7)
Download 30: Solutions to HW10
Download 31: Past Review Problems
Download 32: Solutions to Past Review Problems
Download 33: Past Final Exam
Updates For MATH 305
Jan. 4: Fundamentals of complex variable. Euler's formula. Polar coordinate. Principal value of argument Arg (z).
Jan. 6: Arg (z) and arg (z). De Moivre's formula. Roots of unit. Roots of a complex variable.
Jan. 9: Complex exponential. Sets in the complex plane. Functions of complex variables.
Jan. 11: Functions of complex variables. Image under linear and Mobius map $ w=(a+bz)/ (c+dz)$.
Jan. 13: Image under $w=z^2$. Continuous, differentiable, analytic. Cauchy-Riemann equation.
Jan. 16: Consequences of Cauchy-Riemann equation. Harmonic Functions. Conformal Mapping. Level Sets. More notes can be found here. Lecture Notes on Conformal Mappings
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Lecture Notes 8 Lecture Notes 8-Notes on Integration by Residue Calculus
Lecture Notes 8-5 Lecture Notes 8-5: A Summary
Lecture Notes 9 Lecture Notes 9- Notes on Laurent Series, Singularities and Residue Calculus
Lecture Notes 10 Lecture Notes 10- Notes on Fourier Transforms and Applications
Downloads For MATH305
Download 1: Syllabus
Download 2: HW1 (Due Date: Jan. 13, by 5:30pm)
Download 3: Solutions to HW1
Download 4: HW2 (Due Date: Jan. 23, by 5:30pm)
Download 5: HW3 (Due Date: Jan. 30, by 5:30pm)
Download 6: Solutions to HW2
Download 7: HW4 (Due Date: Feb. 6, by 5:30pm)
Download 8: Solutions to HW3
Download 9: Past Midterm 1-1
Download 10: Past Midterm 1-2
Download 11: Past Midterm 1-3
Download 12: HW5 (Due Date: Feb. 15, by 5:30pm)
Download 13: Solutions to HW4
Download 14: Midterm One and Solutions
Download 15: Solutions to HW5
Download 16: HW6 (Due: Feb. 27)
Download 17: Solutions to HW6
Download 18: HW7 (Due: March 6)
Download 19: Solutions to HW7
Download 20: HW8 (Due: March 13)
Download 21: Solutions to HW8
Download 22: HW9 (Due: March 22)
Download 23: Past Midterm 2-1
Download 24: Past Midterm 2-2
Download 25: Past Midterm 2-3
Download 26: Past Sample Problems
Download 27: Solutions to HW9
Download 28: Solutions to Midterm Examination 2
Download 29: HW10 (Due: April 7)
Download 30: Solutions to HW10
Download 31: Past Review Problems
Download 32: Solutions to Past Review Problems
Download 33: Past Final Exam
Updates For MATH 305
Jan. 4: Fundamentals of complex variable. Euler's formula. Polar coordinate. Principal value of argument Arg (z).
Jan. 6: Arg (z) and arg (z). De Moivre's formula. Roots of unit. Roots of a complex variable.
Jan. 9: Complex exponential. Sets in the complex plane. Functions of complex variables.
Jan. 11: Functions of complex variables. Image under linear and Mobius map $ w=(a+bz)/ (c+dz)$.
Jan. 13: Image under $w=z^2$. Continuous, differentiable, analytic. Cauchy-Riemann equation.
Jan. 16: Consequences of Cauchy-Riemann equation. Harmonic Functions. Conformal Mapping. Level Sets. More notes can be found here. Lecture Notes on Conformal Mappings
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Lecture Notes 8-5 Lecture Notes 8-5: A Summary
Lecture Notes 9 Lecture Notes 9- Notes on Laurent Series, Singularities and Residue Calculus
Lecture Notes 10 Lecture Notes 10- Notes on Fourier Transforms and Applications
Downloads For MATH305
Download 1: Syllabus
Download 2: HW1 (Due Date: Jan. 13, by 5:30pm)
Download 3: Solutions to HW1
Download 4: HW2 (Due Date: Jan. 23, by 5:30pm)
Download 5: HW3 (Due Date: Jan. 30, by 5:30pm)
Download 6: Solutions to HW2
Download 7: HW4 (Due Date: Feb. 6, by 5:30pm)
Download 8: Solutions to HW3
Download 9: Past Midterm 1-1
Download 10: Past Midterm 1-2
Download 11: Past Midterm 1-3
Download 12: HW5 (Due Date: Feb. 15, by 5:30pm)
Download 13: Solutions to HW4
Download 14: Midterm One and Solutions
Download 15: Solutions to HW5
Download 16: HW6 (Due: Feb. 27)
Download 17: Solutions to HW6
Download 18: HW7 (Due: March 6)
Download 19: Solutions to HW7
Download 20: HW8 (Due: March 13)
Download 21: Solutions to HW8
Download 22: HW9 (Due: March 22)
Download 23: Past Midterm 2-1
Download 24: Past Midterm 2-2
Download 25: Past Midterm 2-3
Download 26: Past Sample Problems
Download 27: Solutions to HW9
Download 28: Solutions to Midterm Examination 2
Download 29: HW10 (Due: April 7)
Download 30: Solutions to HW10
Download 31: Past Review Problems
Download 32: Solutions to Past Review Problems
Download 33: Past Final Exam
Updates For MATH 305
Jan. 4: Fundamentals of complex variable. Euler's formula. Polar coordinate. Principal value of argument Arg (z).
Jan. 6: Arg (z) and arg (z). De Moivre's formula. Roots of unit. Roots of a complex variable.
Jan. 9: Complex exponential. Sets in the complex plane. Functions of complex variables.
Jan. 11: Functions of complex variables. Image under linear and Mobius map $ w=(a+bz)/ (c+dz)$.
Jan. 13: Image under $w=z^2$. Continuous, differentiable, analytic. Cauchy-Riemann equation.
Jan. 16: Consequences of Cauchy-Riemann equation. Harmonic Functions. Conformal Mapping. Level Sets. More notes can be found here. Lecture Notes on Conformal Mappings
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Lecture Notes 9 Lecture Notes 9- Notes on Laurent Series, Singularities and Residue Calculus
Lecture Notes 10 Lecture Notes 10- Notes on Fourier Transforms and Applications
Downloads For MATH305
Download 1: Syllabus
Download 2: HW1 (Due Date: Jan. 13, by 5:30pm)
Download 3: Solutions to HW1
Download 4: HW2 (Due Date: Jan. 23, by 5:30pm)
Download 5: HW3 (Due Date: Jan. 30, by 5:30pm)
Download 6: Solutions to HW2
Download 7: HW4 (Due Date: Feb. 6, by 5:30pm)
Download 8: Solutions to HW3
Download 9: Past Midterm 1-1
Download 10: Past Midterm 1-2
Download 11: Past Midterm 1-3
Download 12: HW5 (Due Date: Feb. 15, by 5:30pm)
Download 13: Solutions to HW4
Download 14: Midterm One and Solutions
Download 15: Solutions to HW5
Download 16: HW6 (Due: Feb. 27)
Download 17: Solutions to HW6
Download 18: HW7 (Due: March 6)
Download 19: Solutions to HW7
Download 20: HW8 (Due: March 13)
Download 21: Solutions to HW8
Download 22: HW9 (Due: March 22)
Download 23: Past Midterm 2-1
Download 24: Past Midterm 2-2
Download 25: Past Midterm 2-3
Download 26: Past Sample Problems
Download 27: Solutions to HW9
Download 28: Solutions to Midterm Examination 2
Download 29: HW10 (Due: April 7)
Download 30: Solutions to HW10
Download 31: Past Review Problems
Download 32: Solutions to Past Review Problems
Download 33: Past Final Exam
Updates For MATH 305
Jan. 4: Fundamentals of complex variable. Euler's formula. Polar coordinate. Principal value of argument Arg (z).
Jan. 6: Arg (z) and arg (z). De Moivre's formula. Roots of unit. Roots of a complex variable.
Jan. 9: Complex exponential. Sets in the complex plane. Functions of complex variables.
Jan. 11: Functions of complex variables. Image under linear and Mobius map $ w=(a+bz)/ (c+dz)$.
Jan. 13: Image under $w=z^2$. Continuous, differentiable, analytic. Cauchy-Riemann equation.
Jan. 16: Consequences of Cauchy-Riemann equation. Harmonic Functions. Conformal Mapping. Level Sets. More notes can be found here. Lecture Notes on Conformal Mappings
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Lecture Notes 10 Lecture Notes 10- Notes on Fourier Transforms and Applications
Downloads For MATH305
Download 1: Syllabus
Download 2: HW1 (Due Date: Jan. 13, by 5:30pm)
Download 3: Solutions to HW1
Download 4: HW2 (Due Date: Jan. 23, by 5:30pm)
Download 5: HW3 (Due Date: Jan. 30, by 5:30pm)
Download 6: Solutions to HW2
Download 7: HW4 (Due Date: Feb. 6, by 5:30pm)
Download 8: Solutions to HW3
Download 9: Past Midterm 1-1
Download 10: Past Midterm 1-2
Download 11: Past Midterm 1-3
Download 12: HW5 (Due Date: Feb. 15, by 5:30pm)
Download 13: Solutions to HW4
Download 14: Midterm One and Solutions
Download 15: Solutions to HW5
Download 16: HW6 (Due: Feb. 27)
Download 17: Solutions to HW6
Download 18: HW7 (Due: March 6)
Download 19: Solutions to HW7
Download 20: HW8 (Due: March 13)
Download 21: Solutions to HW8
Download 22: HW9 (Due: March 22)
Download 23: Past Midterm 2-1
Download 24: Past Midterm 2-2
Download 25: Past Midterm 2-3
Download 26: Past Sample Problems
Download 27: Solutions to HW9
Download 28: Solutions to Midterm Examination 2
Download 29: HW10 (Due: April 7)
Download 30: Solutions to HW10
Download 31: Past Review Problems
Download 32: Solutions to Past Review Problems
Download 33: Past Final Exam
Updates For MATH 305
Jan. 4: Fundamentals of complex variable. Euler's formula. Polar coordinate. Principal value of argument Arg (z).
Jan. 6: Arg (z) and arg (z). De Moivre's formula. Roots of unit. Roots of a complex variable.
Jan. 9: Complex exponential. Sets in the complex plane. Functions of complex variables.
Jan. 11: Functions of complex variables. Image under linear and Mobius map $ w=(a+bz)/ (c+dz)$.
Jan. 13: Image under $w=z^2$. Continuous, differentiable, analytic. Cauchy-Riemann equation.
Jan. 16: Consequences of Cauchy-Riemann equation. Harmonic Functions. Conformal Mapping. Level Sets. More notes can be found here. Lecture Notes on Conformal Mappings
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Downloads For MATH305
Download 1: Syllabus
Download 2: HW1 (Due Date: Jan. 13, by 5:30pm)
Download 3: Solutions to HW1
Download 4: HW2 (Due Date: Jan. 23, by 5:30pm)
Download 5: HW3 (Due Date: Jan. 30, by 5:30pm)
Download 6: Solutions to HW2
Download 7: HW4 (Due Date: Feb. 6, by 5:30pm)
Download 8: Solutions to HW3
Download 9: Past Midterm 1-1
Download 10: Past Midterm 1-2
Download 11: Past Midterm 1-3
Download 12: HW5 (Due Date: Feb. 15, by 5:30pm)
Download 13: Solutions to HW4
Download 14: Midterm One and Solutions
Download 15: Solutions to HW5
Download 16: HW6 (Due: Feb. 27)
Download 17: Solutions to HW6
Download 18: HW7 (Due: March 6)
Download 19: Solutions to HW7
Download 20: HW8 (Due: March 13)
Download 21: Solutions to HW8
Download 22: HW9 (Due: March 22)
Download 23: Past Midterm 2-1
Download 24: Past Midterm 2-2
Download 25: Past Midterm 2-3
Download 26: Past Sample Problems
Download 27: Solutions to HW9
Download 28: Solutions to Midterm Examination 2
Download 29: HW10 (Due: April 7)
Download 30: Solutions to HW10
Download 31: Past Review Problems
Download 32: Solutions to Past Review Problems
Download 33: Past Final Exam
Updates For MATH 305
Jan. 4: Fundamentals of complex variable. Euler's formula. Polar coordinate. Principal value of argument Arg (z).
Jan. 6: Arg (z) and arg (z). De Moivre's formula. Roots of unit. Roots of a complex variable.
Jan. 9: Complex exponential. Sets in the complex plane. Functions of complex variables.
Jan. 11: Functions of complex variables. Image under linear and Mobius map $ w=(a+bz)/ (c+dz)$.
Jan. 13: Image under $w=z^2$. Continuous, differentiable, analytic. Cauchy-Riemann equation.
Jan. 16: Consequences of Cauchy-Riemann equation. Harmonic Functions. Conformal Mapping. Level Sets. More notes can be found here. Lecture Notes on Conformal Mappings
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Jan. 6: Arg (z) and arg (z). De Moivre's formula. Roots of unit. Roots of a complex variable.
Jan. 9: Complex exponential. Sets in the complex plane. Functions of complex variables.
Jan. 11: Functions of complex variables. Image under linear and Mobius map $ w=(a+bz)/ (c+dz)$.
Jan. 13: Image under $w=z^2$. Continuous, differentiable, analytic. Cauchy-Riemann equation.
Jan. 16: Consequences of Cauchy-Riemann equation. Harmonic Functions. Conformal Mapping. Level Sets. More notes can be found here. Lecture Notes on Conformal Mappings
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Jan. 9: Complex exponential. Sets in the complex plane. Functions of complex variables.
Jan. 11: Functions of complex variables. Image under linear and Mobius map $ w=(a+bz)/ (c+dz)$.
Jan. 13: Image under $w=z^2$. Continuous, differentiable, analytic. Cauchy-Riemann equation.
Jan. 16: Consequences of Cauchy-Riemann equation. Harmonic Functions. Conformal Mapping. Level Sets. More notes can be found here. Lecture Notes on Conformal Mappings
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Jan. 11: Functions of complex variables. Image under linear and Mobius map $ w=(a+bz)/ (c+dz)$.
Jan. 13: Image under $w=z^2$. Continuous, differentiable, analytic. Cauchy-Riemann equation.
Jan. 16: Consequences of Cauchy-Riemann equation. Harmonic Functions. Conformal Mapping. Level Sets. More notes can be found here. Lecture Notes on Conformal Mappings
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Jan. 13: Image under $w=z^2$. Continuous, differentiable, analytic. Cauchy-Riemann equation.
Jan. 16: Consequences of Cauchy-Riemann equation. Harmonic Functions. Conformal Mapping. Level Sets. More notes can be found here. Lecture Notes on Conformal Mappings
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Jan. 16: Consequences of Cauchy-Riemann equation. Harmonic Functions. Conformal Mapping. Level Sets. More notes can be found here. Lecture Notes on Conformal Mappings
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Jan. 18: Laplace under analytical mappings. $\partial_{\bar{z}} f(z)=0$. Conformal Mappings. Elementary Functions.
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Jan. 20: Elementary functions $ e^z$ and $ \sin (z)$. Images under $ e^z$ and $ sin (z)$.
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Jan. 23: Properties of $\sin z$ and $ sinh (z)$. Introduction of $Log (z)$.
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Jan. 25: Multi-valued functions. introduction of $log (z)$ and $Log (z)$ and their properties.
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Jan. 27: Multi-valued functions. Introduction of $z^\alpha$ and branch cuts.
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Jan. 30: Multi-valued functions. Branch cuts for $ (z^2-1)^{\frac{1}{2}}$.
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Feb. 01: Branch Cuts for $ (z^3-z)^{1/2}, (z^3-z)^{1/3}, (z^2+1)^{1/2}$.
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Feb. 03: Inverse function of sin (z). Solving Laplace equation with Arg (z)
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Feb. 06: Complex integrals. Contours (Paths).
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Feb. 08: Fundamental Theorem of Calculus in the Complex Case. Examples.
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Feb. 10: Midterm 1
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Feb. 15: Cauchy-Coursat Theorem. simply-connected domains. Path independence and deformation of path.
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Feb. 17: Path Independence. Cauchy Integral Formula. Examples.
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Feb. 27: Applications of Cauchy Integral Formula. Computation of real integrals.
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Mar. 1: Consequences of Cauchy Integral Formula. Functions with finite order singularity.
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Mar. 3: Consequences of Cauchy Integral Formula. Liouville Theorem: bounded entire functions are constants.
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
March 6: Maximum Modulus Principle.
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
March 8: Argument Principle, Nyquist Criterion.
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
March 10: Argument Principle, Nyquist criterion, applications to ODE.
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
March 13: Rouche's Theorem (Lecture Note 6-5). Classification of Singularities (Lecture Note 7).
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
March 15: Lecture Note 7. Classification of singularities and computations of residues. See explanations of the notation O(...) here Notation $O(z^m)$
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
March 17: Lecture Note 7. Cauchy Residue Theorem. Computation of residues and contour integrals.
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
March 20: Applications of Cauchy Residue Theorem. Lecture Note 8, page 1-3.
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
March 22: Type I, Type II real integrals.
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
March 24: Midterm 2
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
March 27: Type III real integrals.
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
March 29 Type IV and Type V integrals. Integrals involving Multi-valued functions.
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
April 3: Type V integrals. Finish lecture 8.
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
April 5 (last class): Fourier transforms and inverse Fourier transforms. Two Properties. Applications to ODE and PDE.
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Announcements For MATH 305
New office hour on Jan. 12:4:30-5:30pm
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Coverage for the 1st Midterm: up to Lecture Note 4 on branch cuts and multi-valued functions.
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
New Office Hours on Tuesday (Feb. 7) and Thursday (Feb. 9): Tuesday, 4pm-5pm; Thursday, 4-5:30pm.
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
No office hours during the term break (Feb. 20-24).
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
New deadline for HW9: March 22.
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Coverage for the 2nd Midterm: up to page 6 of Lecture Note 8 on real integrals.
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
New Office Hours on Thursday (March 23): 4-5:30pm.
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
New Office Hours on Thursday (April 6): 4-5:30pm.
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
New Office Hours on April 10, 11, 12, 25, 26: 10am-5pm
Back to My Home Page
Back to My Home Page