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Calendar

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