MATH 305: Applied Complex Analysis

News

• Two additional office hours on Monday, April 16 10-11 and Wednesday April 18, 13-14
• All solutions online
• Assignement 11 (due on Friday, April 6) and Solution 10 are available
• Assignement 10 and Solution 9 are available
• The office hour on Tuesday, March 19 is cancelled due to departmental duties
• The second midterm and its solution are online
• Solution 8 and Assignment 9 posted
• Sign mistake in HW 6, Problem 2(ii) corrected
• Solution 7 available
• Regular office hours moved to 9:00am - 10:00am
• Additional office hour on Friday March 2nd, 1:45pm - 3:15pm
• Assignment 8 posted, due on Monday!
• Solution 6 and Assignment 7 posted
• Solution 5 and Assignment 6 posted
• The midterm and its solution are online
• Assignment 5 is available
• Solution 4 online
• Solution 3 and Assignment 4 (due on Monday!) are available
• Solution 2 and Assignment 3 are available
• Assignments will be returned through the Math Learning Center (MLC), which is also an additional resource for learning support
• Solution 1 and Assignment 2 are available
• Assignment 1 is posted below
• Have a good start in Term 2!

Basic Information

Homework Assignments

 Sheet Number Due Date Solution Assignment 11 April 6 Solution 11 Assignment 10 March 28 Solution 10 Assignment 9 March 21 Solution 9 Assignment 8 March 5 Solution 8 Assignment 7 February 28 Solution 7 Assignment 6 February 14 Solution 6 Assignment 5 February 7 Solution 5 Assignment 4 January 29 Solution 4 Assignment 3 January 24 Solution 3 Assignment 2 January 17 Solution 2 Assignment 1 January 10 Solution 1

Weekly lecture summaries
 Week 13 The Fourier transform: some properties; Application to the solution of the heat equation; Review of the term's material. Week 12 From Taylor series to Fourier series; The Fourier transform. Week 11 Cauchy's integral formula in an annulus; Computing Laurent series: Examples; The Argument Principle; The winding number; Applications. Week 10 Summary and further applications of the Residue Theorem; Short review of the midterm; Laurent series and the classification of singularities. Week 9 The Residue Theorem; Computing residues; Examples; Summary; Application: evaluating convergent series. Week 8 Application of the maximum modulus principle to count zeros; The fundamental theorem of algebra; Taylor series; Holomorphic functions are analytic; Zeros, poles and their multiplicities; The residue. Week 7 Cauchy's integral formula (updated notes); Discussion and an example; Holomorphic functions are infinitely differentiable; The mean value theorem; The maximum modulus principle; The case of harmonic functions. Week 6 Cauchy's theorem (Notes and a proof to be found here); Examples; Review of the midterm. Week 5 Parametrized curves; Definition and examples; Integration of complex functions; Definition and examples; An upper bound; The case of functions with an antiderivative; Path independence. Week 4 Trigonometric and hyperbolic functions; The multivalued logarithm; The principal branch of general powers; The multivalued square root; Outlook on Riemann surfaces; Dynamics of driven oscillating systems. Week 3 The Cauchy-Riemann equations; Conjugate harmonic functions; Examples; The exponential and the logarithm. Week 2 More on the complex exponential; Subsets: bounded, open connected; Complex functions; Examples; Continuity: Definition and examples; Differentiability; Holomorphic functions. Week 1 Introduction; The set of complex numbers; The complex conjugate, inverses; The absolute value and the argument; The complex exponential; Trigonometric identities.