Transform Techniques For Engineers

About Course

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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Course Content

Transform Techniques for Engineers

Use of Delta function in the Fourier series convergence

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Fourier series – Examples

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Complex Fourier series

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Conditions for the Convergence of Fourier Series

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Conditions for the Convergence of Fourier Series(continued)

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Introduction to Fourier series

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More Examples on Fourier Series of a Periodic Signal

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Gibb’s Phenomenon in the Computation of Fourier Series

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Properties of Fourier Transform of a Periodic Signal

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Properties of Fourier transform (continued)

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Parseval’s Identity and Recap of Fourier series

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Fourier integral theorem-an informal proof

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Definition of Fourier transforms

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Fourier transform of a Heavyside function

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Use of Fourier transforms to evaluate some integrals

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Evaluation of an integral- Recall of complex function theory

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Properties of Fourier transforms of non-periodic signals

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More properties of Fourier transforms

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Fourier integral theorem – proof

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Application of Fourier transform to ODE’s

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Application of Fourier transforms to differential and integral equations

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Evaluation of integrals by Fourier transforms

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D’Alembert’s solution by Fourier transform

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Solution of Heat equation by Fourier transform

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Solution of Heat and Laplace equations by Fourier transform

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Introduction to Laplace transform

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Laplace transform of elementary functions

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Properties of Laplace transforms

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Properties of Laplace transforms (continued)

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Methods of finding inverse Laplace transform

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Heavyside expansion theorem

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Review of complex function theory

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Inverse Laplace transform by contour integration

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Application of Laplace transforms-ODEs’

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Solutions of initial or boundary value problems for ODEs’

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Solving first order PDE’s by Laplace transform

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Solution of wave equation by Laplace transform

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Solving hyperbolic equations by Laplace transform

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Solving heat equation by Laplace transform

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Initial boundary value problems for heat equations

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Solution of integral equations by Laplace transform

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Evaluation of integrals by Laplace transform

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Introduction to Z-transforms

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Properties of Z-transforms

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conclusions

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Evaluation of infinite sums by Z-transformson

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Solution of difference equations by Z-transforms

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Inverse Z-transforms

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About Course

Transform Techniques.

What Will You Learn?

Course Content

Transform Techniques for Engineers

Use of Delta function in the Fourier series convergence

Fourier series – Examples

Complex Fourier series

Conditions for the Convergence of Fourier Series

Conditions for the Convergence of Fourier Series(continued)

Introduction to Fourier series

More Examples on Fourier Series of a Periodic Signal

Gibb’s Phenomenon in the Computation of Fourier Series

Properties of Fourier Transform of a Periodic Signal

Properties of Fourier transform (continued)

Parseval’s Identity and Recap of Fourier series

Fourier integral theorem-an informal proof

Definition of Fourier transforms

Fourier transform of a Heavyside function

Use of Fourier transforms to evaluate some integrals

Evaluation of an integral- Recall of complex function theory

Properties of Fourier transforms of non-periodic signals

More properties of Fourier transforms

Fourier integral theorem – proof

Application of Fourier transform to ODE’s

Application of Fourier transforms to differential and integral equations

Evaluation of integrals by Fourier transforms

D’Alembert’s solution by Fourier transform

Solution of Heat equation by Fourier transform

Solution of Heat and Laplace equations by Fourier transform

Introduction to Laplace transform

Laplace transform of elementary functions

Properties of Laplace transforms

Properties of Laplace transforms (continued)

Methods of finding inverse Laplace transform

Heavyside expansion theorem

Review of complex function theory

Inverse Laplace transform by contour integration

Application of Laplace transforms-ODEs’

Solutions of initial or boundary value problems for ODEs’

Solving first order PDE’s by Laplace transform

Solution of wave equation by Laplace transform

Solving hyperbolic equations by Laplace transform

Solving heat equation by Laplace transform

Initial boundary value problems for heat equations

Solution of integral equations by Laplace transform

Evaluation of integrals by Laplace transform

Introduction to Z-transforms

Properties of Z-transforms

conclusions

Evaluation of infinite sums by Z-transformson

Solution of difference equations by Z-transforms

Inverse Z-transforms

Student Ratings & Reviews