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Course11110611147 lectures

Transform Techniques for Engineers

Prof. Srinivasa Rao Manam · IIT Madras

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Introduction to Fourier series Video
  2. Fourier series - Examples Video
  3. Complex Fourier series Video
  4. Conditions for the Convergence of Fourier Series Video
  5. Conditions for the Convergence of Fourier Series(continued) Video

Week 2

  1. Use of Delta function in the Fourier series convergence Video
  2. More Examples on Fourier Series of a Periodic Signal Video
  3. Gibb's Phenomenon in the Computation of Fourier Series Video
  4. Properties of Fourier Transform of a Periodic Signal Video
  5. Properties of Fourier transform (continued) Video

Week 3

  1. Parseval's Identity and Recap of Fourier series Video
  2. Fourier integral theorem-an informal proof Video
  3. Definition of Fourier transforms Video
  4. Fourier transform of a Heavyside function Video
  5. Use of Fourier transforms to evaluate some integrals Video

Week 4

  1. Evaluation of an integral- Recall of complex function theory Video
  2. Properties of Fourier transforms of non-periodic signals Video
  3. More properties of Fourier transforms Video
  4. Fourier integral theorem - proof Video

Week 5

  1. Application of Fourier transform to ODE's Video
  2. Application of Fourier transforms to differential and integral equations Video
  3. Evaluation of integrals by Fourier transforms Video
  4. D'Alembert's solution by Fourier transform Video

Week 6

  1. Solution of Heat equation by Fourier transform Video
  2. Introduction to Laplace transform Video
  3. Laplace transform of elementary functions Video

Week 7

  1. Properties of Laplace transforms Video
  2. Properties of Laplace transforms (continued) Video
  3. Methods of finding inverse Laplace transform Video

Week 8

  1. Heavyside expansion theorem Video
  2. Review of complex function theory Video
  3. Inverse Laplace transform by contour integration Video

Week 9

  1. Application of Laplace transforms-ODEs' Video
  2. Solutions of initial or boundary value problems for ODEs' Video
  3. Solving first order PDE's by Laplace transform Video

Week 10

  1. Solution of wave equation by Laplace transform Video
  2. Solving hyperbolic equations by Laplace transform Video
  3. Solving heat equation by Laplace transform Video
  4. Initial boundary value problems for heat equations Video

Week 11

  1. Solution of integral equations by Laplace transform Video
  2. Evaluation of integrals by Laplace transform Video
  3. Introduction to Z-transforms Video
  4. Properties of Z-transforms Video

How to access the portal

  1. Inverse Z-transforms Video
  2. Solution of difference equations by Z-transforms Video
  3. Evaluation of infinite sums by Z-transforms Video
  4. conclusions Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Madras
Department
Mathematics
Teacher
Prof. Srinivasa Rao Manam
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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