Syllabus for 18.04
- Two Lectures: Ordinary Differential Equations ( Read Chapter 1.)
- One Lecture: Complex Numbers. ( Read Sec. A, Chapter 2).
- Two Lectures: Operators and Ordinary Differential Equations. (Read Chapter 1).
- Two lectures: Analytic Functions, Cauchy--Riemann Equations. ( Read 2A and 2B).
- Two lectures: Cauchy Integral Theorem, Taylor Series, Laurent Series. ( Read 2C).
- Five lectures: Evaluation of Real Integrals. ( Read 2D).
- Three lectures: Branch Cuts and Branch Points. (Read 2E).
- One lecture: Rouche's theorem and Liouville's theorem
- Five lectures: Fourier Integrals, Fourier Series, and Laplace transform. (Read 2F and 2G).
- One lecture: Sturm-Liouville problem
- Six lectures: Partial differential Equations.
Other topics such as series solutions of ordinary differential equations may also be included if time permits.