Course outline: The course divides into 3 parts, ODEs, PDEs and complex analysis. Related topics such as Special functions, Fourier series and Transforms and
Green's functions will be covered.
Evaluation for this course: 2 quizzes 15 % each, Mid-semester exam 35 %, Final exam 35%, except for Ph.D students. For them, each quiz will be worth 10% and a project presentation or assignments worth 10%.
OFFICE HOURS: Wednesday 3:30-4:30 PM. This will be the meeting hour (in my office) if
you have any questions related to the course. Any other meeting hours by prior appointment only - email me for an appointment.
Voluntary attendance tutorials will also take place in this slot.
Suggested books:
1. Differential equations: Simmons (Chapter 4 contains material on qualitative analysis of ODES). This is for ODEs.
2. Ordinary Differential equations: Birkhoff and Rota
3. Fourier transforms: Arfken and other math methods books.
4. Partial differential equations and Green's functions for operators with no time derivatives: Myint-U and Debnath (available as e-book
in our library).
5. Green's functions for operators with time derivatives, causal Green's functions: class notes
6. Complex analysis, contour integration: Saff and Snider for the material. Schaum series in
complex analysis (author Spiegel) is excellent and has many solved problems for practice.
7. Complex/conformal mappings: Saff and Snider.
Assignment 1 here.
Assignment 2 here.
Assignment 3 here.
Quiz 1 on Sep. 5 in class. Includes everything until and including series
solutions to ODEs. Laplace transform formula sheet will be provided.
Midterm: Includes everything done so far except Green's functions.
Assignment 4 here.
Assignment 5 here.