| 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 |
