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