Transform Techniques for Engineers (Dr. Srinivasa Rao Manam, IIT Madras) | Mathematics

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)

Introduction to Fourier Series

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

References

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.