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Lecture Notes

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)