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Transform Techniques for Engineers

Transform Techniques for Engineers. Instructors: Dr. Srinivasa Rao Manam, Department of Mathematics, IIT Madras. The aim of the course is to teach various transform techniques that are essential for a student of physical sciences and engineering. They include Fourier series, Fourier transform, Laplace transform, and z-transform. (from nptel.ac.in)

Lecture 41 - Solution of Integral Equations by Laplace Transform


Go to the Course Home or watch other lectures:

Lecture 01 - Introduction to Fourier Series
Lecture 02 - Fourier Series: Examples
Lecture 03 - Complex Fourier Series
Lecture 04 - Conditions for the Convergence of Fourier Series
Lecture 05 - Conditions for the Convergence of Fourier Series (cont.)
Lecture 06 - Use of Delta Function in the Fourier Series Convergence
Lecture 07 - More Examples on Fourier Series of a Periodic Signal
Lecture 08 - Gibb's Phenomenon in the Computation of Fourier Series
Lecture 09 - Properties of Fourier Transform of a Periodic Signal
Lecture 10 - Properties of Fourier Transform (cont.)
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 Heaviside 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 ODEs
Lecture 21 - Application of Fourier Transforms to Differential and Integral Equations
Lecture 22 - Evaluations 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 (cont.)
Lecture 30 - Methods of Finding Inverse Laplace Transform
Lecture 31 - Heaviside Expansion Theorem
Lecture 32 - Review of Complex Function Theory
Lecture 33 - Inverse Laplace Transform by Contour Integration
Lecture 34 - Application of Laplace Transform - ODEs
Lecture 35 - Solution of Initial or Boundary Value Problems for ODEs
Lecture 36 - Solving First Order PDEs 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 - Evaluation of Infinite Sums by z-Transforms
Lecture 46 - Solution of Difference Equations by z-Transforms
Lecture 47 - Inverse z-Transforms
Lecture 48 - Conclusions