# Syllabus

**Two Lectures:** Operators and Ordinary Differential Equations. (Read Chapter 1).

**Two lectures:** Complex Numbers, 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).

**Two lectures:** Branch Cuts and Brabch Points. (Read 2E).

**Four lectures:** Fourier Integrals, Fourier Series, and Laplace transform. (Read 2F and 2G).

**Four lectures:** First Order PDE. ( Read Chapter 3 selectively).

**Four lectures:** Second Order Partial Differential Equations, Eigenfunctions, and Eigenvalues. (Read Chapter 4 selectively).

**Three lectures:** Separation of varaiables (Read Chapter 5).

**One lecture:** Eigenfunctions, and Eigenvalues. (Read Chapter 5).

**Three lectures:** Taylor Series Solutions. (Read 6A).

**Three lectures:** Frobenius Series. (Read 6B).

**One lecture:** Irregular Singular Points. (Read 6C).