1 | Introduction to Fourier series | PDF unavailable |
2 | Fourier series - Examples | PDF unavailable |
3 | Complex Fourier series | PDF unavailable |
4 | Conditions for the Convergence of Fourier Series | PDF unavailable |
5 | Conditions for the Convergence of Fourier Series(continued) | PDF unavailable |
6 | Use of Delta function in the Fourier series convergence | PDF unavailable |
7 | More Examples on Fourier Series of a Periodic Signal | PDF unavailable |
8 | Gibb's Phenomenon in the Computation of Fourier Series | PDF unavailable |
9 | Properties of Fourier Transform of a Periodic Signal | PDF unavailable |
10 | Properties of Fourier transform (continued) | PDF unavailable |
11 | Parseval's Identity and Recap of Fourier series | PDF unavailable |
12 | Fourier integral theorem-an informal proof | PDF unavailable |
13 | Definition of Fourier transforms | PDF unavailable |
14 | Fourier transform of a Heavyside function | PDF unavailable |
15 | Use of Fourier transforms to evaluate some integrals | PDF unavailable |
16 | Evaluation of an integral- Recall of complex function theory | PDF unavailable |
17 | Properties of Fourier transforms of non-periodic signals | PDF unavailable |
18 | More properties of Fourier transforms | PDF unavailable |
19 | Fourier integral theorem - proof | PDF unavailable |
20 | Application of Fourier transform to ODE's | PDF unavailable |
21 | Application of Fourier transforms to differential and integral equations | PDF unavailable |
22 | Evaluation of integrals by Fourier transforms | PDF unavailable |
23 | D'Alembert's solution by Fourier transform | PDF unavailable |
24 | Solution of Heat equation by Fourier transform | PDF unavailable |
25 | Solution of Heat and Laplace equations by Fourier transform | PDF unavailable |
26 | Introduction to Laplace transform | PDF unavailable |
27 | Laplace transform of elementary functions | PDF unavailable |
28 | Properties of Laplace transforms | PDF unavailable |
29 | Properties of Laplace transforms (continued) | PDF unavailable |
30 | Methods of finding inverse Laplace transform | PDF unavailable |
31 | Heavyside expansion theorem | PDF unavailable |
32 | Review of complex function theory | PDF unavailable |
33 | Inverse Laplace transform by contour integration | PDF unavailable |
34 | Application of Laplace transforms-ODEs' | PDF unavailable |
35 | Solutions of initial or boundary value problems for ODEs' | PDF unavailable |
36 | Solving first order PDE's by Laplace transform | PDF unavailable |
37 | Solution of wave equation by Laplace transform | PDF unavailable |
38 | Solving hyperbolic equations by Laplace transform | PDF unavailable |
39 | Solving heat equation by Laplace transform | PDF unavailable |
40 | Initial boundary value problems for heat equations | PDF unavailable |
41 | Solution of integral equations by Laplace transform | PDF unavailable |
42 | Evaluation of integrals by Laplace transform | PDF unavailable |
43 | Introduction to Z-transforms | PDF unavailable |
44 | Properties of Z-transforms | PDF unavailable |
45 | Inverse Z-transforms | PDF unavailable |
46 | Solution of difference equations by Z-transforms | PDF unavailable |
47 | Evaluation of infinite sums by Z-transforms | PDF unavailable |
48 | conclusions | PDF unavailable |