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Advanced Calculus for Engineers >> Content Detail



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Calendar

LEC #TOPICS
1Number Systems and Algebra of Complex Numbers
2Elementary Complex Functions, Part 1
3Elementary Complex Functions, Part 2
4Branch Points and Branch Cuts
5Analytic Functions
6Complex Integrals
7Cauchy's Formula, Properties of Analytic Functions
8Taylor Series, Laurent Series
9Laurent Series (cont.)
10Properties of Laurent Series, Singularities
11Singularities (cont.)
12Residue Theorem
13In-class exam 1
14Evaluation of Real Definite Integrals, Case I
15Evaluation of Real Definite Integrals, Case II
16Evaluation of Real Definite Integrals, Case III
17Evaluation of Real Definite Integrals, Case IV
18Theorems for Contour Integration
19Series and Convergence
20Ordinary Differential Equations
21Singular Points of Linear Second-Order ODEs
22Frobenius Method
23Frobenius Method - Examples
24Frobenius Method (cont.) and a "particular type" of ODE
25Bessel Functions
26Properties of Bessel Functions
27Modified Bessel Functions
28In-class exam 2
29Differential Equations Satisfied by Bessel Functions
30Introduction to Boundary-Value Problems
31Eigenvalues, Eigenfunctions, Orthogonality of Eigenfunctions
32Boundary Value Problems for Nonhomogeneous PDEs
33Sturm-Liouville Problem
34Fourier Series
35Fourier Sine and Cosine Series
36Complete Fourier Series
37Review of Boundary Value Problems for Nonhomogeneous PDEs
38In-class exam 3

 








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