Lecture 1 - Introduction to Fourier series

Lecture 2 - Fourier series - Examples

Lecture 3 - Complex Fourier series

Lecture 4 - Conditions for the Convergence of Fourier Series

Lecture 5 - Conditions for the Convergence of Fourier Series (Continued...)

Lecture 6 - Use of Delta function in the Fourier series convergence

Lecture 7 - More Examples on Fourier Series of a Periodic Signal

Lecture 8 - Gibb's Phenomenon in the Computation of Fourier Series

Lecture 9 - Properties of Fourier Transform of a Periodic Signal

Lecture 10 - Properties of Fourier transform (Continued...)

Lecture 11 - Parseval's Identity and Recap of Fourier series

Lecture 12 - Fourier integral theorem-an informal proof

Lecture 13 - Definition of Fourier transforms

Lecture 14 - Fourier transform of a Heavyside function

Lecture 15 - Use of Fourier transforms to evaluate some integrals

Lecture 16 - Evaluation of an integral- Recall of complex function theory

Lecture 17 - Properties of Fourier transforms of non-periodic signals

Lecture 18 - More properties of Fourier transforms

Lecture 19 - Fourier integral theorem - proof

Lecture 20 - Application of Fourier transform to ODE's

Lecture 21 - Application of Fourier transforms to differential and integral equations

Lecture 22 - Evaluation of integrals by Fourier transforms

Lecture 23 - D'Alembert's solution by Fourier transform

Lecture 24 - Solution of Heat equation by Fourier transform

Lecture 25 - Solution of Heat and Laplace equations by Fourier transform

Lecture 26 - Introduction to Laplace transform

Lecture 27 - Laplace transform of elementary functions

Lecture 28 - Properties of Laplace transforms

Lecture 29 - Properties of Laplace transforms (Continued...)

Lecture 30 - Methods of finding inverse Laplace transform

Lecture 31 - Heavyside expansion theorem

Lecture 32 - Review of complex function theory

Lecture 33 - Inverse Laplace transform by contour integration

Lecture 34 - Application of Laplace transforms - ODEs'

Lecture 35 - Solutions of initial or boundary value problems for ODEs'

Lecture 36 - Solving first order PDE's by Laplace transform

Lecture 37 - Solution of wave equation by Laplace transform

Lecture 38 - Solving hyperbolic equations by Laplace transform

Lecture 39 - Solving heat equation by Laplace transform

Lecture 40 - Initial boundary value problems for heat equations

Lecture 41 - Solution of Integral Equations by Laplace Transform

Lecture 42 - Evaluation of Integrals by Laplace Transform

Lecture 43 - Introduction to Z-Transforms

Lecture 44 - Properties of Z-Transforms

Lecture 45 - Inverse Z-transforms

Lecture 46 - Solution of difference equations by Z-transforms

Lecture 47 - Evaluation of infinite sums by Z-transforms

Lecture 48 - conclusions