| LEC # | TOPICS |
|---|---|
| 1 | Number Systems and Algebra of Complex Numbers |
| 2 | Elementary Complex Functions, Part 1 |
| 3 | Elementary Complex Functions, Part 2 |
| 4 | Branch Points and Branch Cuts |
| 5 | Analytic Functions |
| 6 | Complex Integrals |
| 7 | Cauchy's Formula, Properties of Analytic Functions |
| 8 | Taylor Series, Laurent Series |
| 9 | Laurent Series (cont.) |
| 10 | Properties of Laurent Series, Singularities |
| 11 | Singularities (cont.) |
| 12 | Residue Theorem |
| 13 | In-class exam 1 |
| 14 | Evaluation of Real Definite Integrals, Case I |
| 15 | Evaluation of Real Definite Integrals, Case II |
| 16 | Evaluation of Real Definite Integrals, Case III |
| 17 | Evaluation of Real Definite Integrals, Case IV |
| 18 | Theorems for Contour Integration |
| 19 | Series and Convergence |
| 20 | Ordinary Differential Equations |
| 21 | Singular Points of Linear Second-Order ODEs |
| 22 | Frobenius Method |
| 23 | Frobenius Method - Examples |
| 24 | Frobenius Method (cont.) and a "particular type" of ODE |
| 25 | Bessel Functions |
| 26 | Properties of Bessel Functions |
| 27 | Modified Bessel Functions |
| 28 | In-class exam 2 |
| 29 | Differential Equations Satisfied by Bessel Functions |
| 30 | Introduction to Boundary-Value Problems |
| 31 | Eigenvalues, Eigenfunctions, Orthogonality of Eigenfunctions |
| 32 | Boundary Value Problems for Nonhomogeneous PDEs |
| 33 | Sturm-Liouville Problem |
| 34 | Fourier Series |
| 35 | Fourier Sine and Cosine Series |
| 36 | Complete Fourier Series |
| 37 | Review of Boundary Value Problems for Nonhomogeneous PDEs |
| 38 | In-class exam 3 |