Advanced Calculus for Engineers

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