NOC:Transform Techniques for Engineers


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