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 Ztransforms.
Course outline
1Introduction to Fourier series
2Finding Fourier series of a periodic function
3Fourier transforms over the real line
4Fourier transform and its properties
5Fourier transform and its applications
6Preliminaries on complex variable techniques
7Introduction to Laplace transform
8Laplace transform and its properties
9Laplace transform and its properties
10Laplace transform and its applications to ODE and PDEs
11Ztransforms
12Ztransforms and its properties and applications
Course Content
Transform Techniques for Engineers

Inverse Ztransforms
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Solutions of initial or boundary value problems for ODEs’
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Application of Laplace transformsODEs’
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Inverse Laplace transform by contour integration
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Review of complex function theory
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Heavyside expansion theorem
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Methods of finding inverse Laplace transform
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Properties of Laplace transforms (continued)
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Properties of Laplace transforms
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Laplace transform of elementary functions
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Introduction to Laplace transform
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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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Solution of difference equations by Ztransforms
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Evaluation of infinite sums by Ztransformson
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conclusions
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Properties of Ztransforms
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Introduction to Ztransforms
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Evaluation of integrals by Laplace transform
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Solution of integral equations by Laplace transform
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Initial boundary value problems for heat equations
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Solving heat equation by Laplace transform
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Solving hyperbolic equations by Laplace transform
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Solution of Heat and Laplace equations by Fourier transform
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Solution of Heat equation by Fourier transform
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Parseval’s Identity and Recap of Fourier series
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Properties of Fourier transform (continued)
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Properties of Fourier Transform of a Periodic Signal
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Gibb’s Phenomenon in the Computation of Fourier Series
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More Examples on Fourier Series of a Periodic Signal
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Introduction to Fourier series
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Conditions for the Convergence of Fourier Series(continued)
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Conditions for the Convergence of Fourier Series
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Complex Fourier series
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Fourier series – Examples
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Fourier integral theoreman informal proof
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Definition of Fourier transforms
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D’Alembert’s solution by Fourier transform
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Evaluation of integrals by Fourier transforms
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Application of Fourier transforms to differential and integral equations
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Application of Fourier transform to ODE’s
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Fourier integral theorem – proof
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More properties of Fourier transforms
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Properties of Fourier transforms of nonperiodic signals
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Evaluation of an integral Recall of complex function theory
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Use of Fourier transforms to evaluate some integrals
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Fourier transform of a Heavyside function
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Use of Delta function in the Fourier series convergence
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