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September 23, 2023

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Description

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)

Course Curriculum

  • Lecture 01 – Introduction to Fourier Series Unlimited
  • Lecture 02 – Fourier Series: Examples Unlimited
  • Lecture 03 – Complex Fourier Series Unlimited
  • Lecture 04 – Conditions for the Convergence of Fourier Series Unlimited
  • Lecture 05 – Conditions for the Convergence of Fourier Series (cont.) Unlimited
  • Lecture 06 – Use of Delta Function in the Fourier Series Convergence Unlimited
  • Lecture 07 – More Examples on Fourier Series of a Periodic Signal Unlimited
  • Lecture 08 – Gibb’s Phenomenon in the Computation of Fourier Series Unlimited
  • Lecture 09 – Properties of Fourier Transform of a Periodic Signal Unlimited
  • Lecture 10 – Properties of Fourier Transform (cont.) Unlimited
  • Lecture 11 – Parseval’s Identity and Recap of Fourier Series Unlimited
  • Lecture 12 – Fourier Integral Theorem – an Informal Proof Unlimited
  • Lecture 13 – Definition of Fourier Transforms Unlimited
  • Lecture 14 – Fourier Transform of a Heaviside Function Unlimited
  • Lecture 15 – Use of Fourier Transforms to Evaluate Some Integrals Unlimited
  • Lecture 16 – Evaluation of an Integral – Recall of Complex Function Theory Unlimited
  • Lecture 17 – Properties of Fourier Transforms of Non-periodic Signals Unlimited
  • Lecture 18 – More Properties of Fourier Transforms Unlimited
  • Lecture 19 – Fourier Integral Theorem – Proof Unlimited
  • Lecture 20 – Application of Fourier Transform to ODEs Unlimited
  • Lecture 21 – Application of Fourier Transforms to Differential and Integral Equations Unlimited
  • Lecture 22 – Evaluations of Integrals by Fourier Transforms Unlimited
  • Lecture 23 – D’Alembert’s Solution by Fourier Transform Unlimited
  • Lecture 24 – Solution of Heat Equation by Fourier Transform Unlimited
  • Lecture 25 – Solution of Heat and Laplace Equations by Fourier Transform Unlimited
  • Lecture 26 – Introduction to Laplace Transform Unlimited
  • Lecture 27 – Laplace Transform of Elementary Functions Unlimited
  • Lecture 28 – Properties of Laplace Transforms Unlimited
  • Lecture 29 – Properties of Laplace Transforms (cont.) Unlimited
  • Lecture 30 – Methods of Finding Inverse Laplace Transform Unlimited
  • Lecture 31 – Heaviside Expansion Theorem Unlimited
  • Lecture 32 – Review of Complex Function Theory Unlimited
  • Lecture 33 – Inverse Laplace Transform by Contour Integration Unlimited
  • Lecture 34 – Application of Laplace Transform – ODEs Unlimited
  • Lecture 35 – Solution of Initial or Boundary Value Problems for ODEs Unlimited
  • Lecture 36 – Solving First Order PDEs by Laplace Transform Unlimited
  • Lecture 37 – Solution of Wave Equation by Laplace Transform Unlimited
  • Lecture 38 – Solving Hyperbolic Equations by Laplace Transform Unlimited
  • Lecture 39 – Solving Heat Equation by Laplace Transform Unlimited
  • Lecture 40 – Initial Boundary Value Problems for Heat Equations Unlimited
  • Lecture 41 – Solution of Integral Equations by Laplace Transform Unlimited
  • Lecture 42 – Evaluation of Integrals by Laplace Transform Unlimited
  • Lecture 43 – Introduction to z-Transforms Unlimited
  • Lecture 44 – Properties of z-Transforms Unlimited
  • Lecture 45 – Evaluation of Infinite Sums by z-Transforms Unlimited
  • Lecture 46 – Solution of Difference Equations by z-Transforms Unlimited
  • Lecture 47 – Inverse z-Transforms Unlimited
  • Lecture 48 – Conclusions Unlimited

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