MATH256-103 : Differential Equations (First term 2014/2015)
Lecture I: Monday 14:00--15:00, Math 100.
Lecture II: Wednesday 14:00--15:00, Math 100.
Lecture III: Friday 14:00--15:00, Math 100.
Office Hours: MON, 4:40-5:30, WED, 4:40-5:30, THURS, 1-1:50. Location: MATX 1118
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Updates For MATH 256
September 3rd, 2014: First class
September 3d: Chapter 1. Introduced ODE, the order, general and particular solutions, linear.
Sept. 5: Chapter 2.1: First order linear equation. Two ways to derive the formula. Three examples. Remember the formula!
Sept 8: Two problems in Section 2.1. Interval of Existence: check a) the solution, b) the equation, c) the initial condition. Separable Equations (2.2). Three problems in Section 2.2.
Sept. 10: Three problems on separable equations. Difference between linear and nonlinear ODEs (2.4). Homogeneous ODEs.
Sept. 12: Modelling with ODEs (2.3, 2.5). Example 1: Bank. Example 2: rockets. Example 3: population dynamics.
Sept 15: More on Example 3. Section 3.1 and 3.2. Finished with the definition of Wronskian.
Sept. 17: Finished 3.2 on the theory of fundamental solutions. Start on 3.3.
Sept. 19: Finished 3.3 and 3.4. Reduction of Order.
Sept. 24: Method of Undetermined Coefficients (3.5). Examples.
Sept 26: Method of Variation of Parameters (3.6). Examples.
Sept. 29: Spring-Mass system (3.7). Three Cases.
Oct. 1: Spring-Mass system (3.8). Review for Midterm.
Oct. 3: Midterm Test
Oct. 6: Section 7.3. Eigenvalues, Eigenvectors, Algebraic multiplicity, geometric multiplicity. Please do more examples by yourself.
Oct. 8: Section 7.4: Basic Theory of Systems of Linear ODEs. Abel's formula: $W^{'} (t)= (p_{11}+...+ p_{nn} ) W$. Three definitions.
Oct. 10: Section 7.4. Start on Section 7.5.
Oct. 15: Section 7.6. Started on Section 7.8.
Oct. 17: Section 7.7, Section 7.8.
Oct. 20: Section 7.9. Method of Diagonalization and Method of Undetermined Coefficients.
Oct. 22: Section 7.9: Method of Variation of Parameters. Please check the appendix for complete solutions of Example 2.
Oct. 24: Section 6.1. Laplace transform. Definitions and five examples.
Oct. 27: Section 6.2: Properties of Laplace Transform, Inverse Laplace Transform, Method of Partial Fractions.
Oct. 29: Finished Section 6.2. Started on Section 6.3: Discontinuous Functions.
Oct. 31: Section 6.3 and Section 6.4.
Nov. 3: Section 6.4, Section 6.5.
Nov. 5: Section 6.5, 6.6.
Nov. 7: Section 10.1
Nov. 10: Section 10.2, 10.3.
Nov. 12: Section 10.3, 10.4.
Nov. 14: started on 10.5. Review of Chapter 6 and 7.
Nov. 17: Midterm Test Two.
Nov. 19: 10.5
Nov. 21: 10.6
Nov. 24: 10.6, 10. 7
Nov. 26: 10. 8 < h3>
Nov. 28: Review for final exam.
Announcements For MATH 256-103
Office Hours are: MON, 4:40-5:30, WED, 4:40-5:30, THURS, 1-1:50. Location: MATX 1118
Coverage of Midterm Test 1: Chapter 1, 2.1-2.5, 3.1-3.6.
Mean of Midterm Test 1: 68.5
Deadline of HW#5 is extended to Oct. 27 !
For HW#6, problem 7.9, 3: use the method of variation of parameters. You will get full marks for whatever method, as long as you can solve it.
New deadline for handing in HW#9: 6pm on Dec. 2.
Office Hours in the week of Dec. 1-5: I will hold office hours on Dec.1, 2, and 3 at room MATH Annex 1118 from 4pm to 5pm.
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