# InfoCoBuild

## 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.