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Transform Techniques for Engineers

  • Course level: Intermediate
  • Categories C-Science
  • Last Update 24/06/2021

Description

Transform Techniques.

Course Intro: 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 transforms, Laplace transform,s and Z-transforms.

Course outline

1-Introduction to Fourier series

2-Finding Fourier series of a periodic function

3-Fourier transforms over the real line

4-Fourier transform and its properties

5-Fourier transform and its applications

6-Preliminaries on complex variable techniques

7-Introduction to Laplace transform

8-Laplace transform and its properties

9-Laplace transform and its properties

10-Laplace transform and its applications to ODE and PDEs

11-Z-transforms

12-Z-transforms and its properties and applications

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What Will I Learn?

  • Learn the various transform techniques that are essential for a student of physical sciences and engineering. They include Fourier series, Fourier transforms, Laplace transform,s and Z-transforms.

Topics for this course

48 Lessons

Transform Techniques for Engineers

Use of Delta function in the Fourier series convergence00:00:00
Fourier series – Examples00:00:00
Complex Fourier series00:00:00
Conditions for the Convergence of Fourier Series00:00:00
Conditions for the Convergence of Fourier Series(continued)00:00:00
Introduction to Fourier series00:00:00
More Examples on Fourier Series of a Periodic Signal00:00:00
Gibb’s Phenomenon in the Computation of Fourier Series00:00:00
Properties of Fourier Transform of a Periodic Signal00:00:00
Properties of Fourier transform (continued)00:00:00
Parseval’s Identity and Recap of Fourier series00:00:00
Fourier integral theorem-an informal proof00:00:00
Definition of Fourier transforms00:00:00
Fourier transform of a Heavyside function00:00:00
Use of Fourier transforms to evaluate some integrals00:00:00
Evaluation of an integral- Recall of complex function theory00:00:00
Properties of Fourier transforms of non-periodic signals00:00:00
More properties of Fourier transforms00:00:00
Fourier integral theorem – proof00:00:00
Application of Fourier transform to ODE’s00:00:00
Application of Fourier transforms to differential and integral equations00:00:00
Evaluation of integrals by Fourier transforms00:00:00
D’Alembert’s solution by Fourier transform00:00:00
Solution of Heat equation by Fourier transform00:00:00
Solution of Heat and Laplace equations by Fourier transform00:00:00
Introduction to Laplace transform00:00:00
Laplace transform of elementary functions00:00:00
Properties of Laplace transforms00:00:00
Properties of Laplace transforms (continued)00:00:00
Methods of finding inverse Laplace transform00:00:00
Heavyside expansion theorem00:00:00
Review of complex function theory00:00:00
Inverse Laplace transform by contour integration00:00:00
Application of Laplace transforms-ODEs’00:00:00
Solutions of initial or boundary value problems for ODEs’00:00:00
Solving first order PDE’s by Laplace transform00:00:00
Solution of wave equation by Laplace transform00:00:00
Solving hyperbolic equations by Laplace transform00:00:00
Solving heat equation by Laplace transform00:00:00
Initial boundary value problems for heat equations00:00:00
Solution of integral equations by Laplace transform00:00:00
Evaluation of integrals by Laplace transform00:00:00
Introduction to Z-transforms00:00:00
Properties of Z-transforms00:00:00
conclusions00:00:00
Evaluation of infinite sums by Z-transformson00:00:00
Solution of difference equations by Z-transforms00:00:00
Inverse Z-transforms00:00:00
Transform Techniques
Free

Enrolment validity: Lifetime