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).