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

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 theoreman 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 nonperiodic 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 transformsODEs’
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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 Ztransforms
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Properties of Ztransforms
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conclusions
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Evaluation of infinite sums by Ztransformson
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Solution of difference equations by Ztransforms
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Inverse Ztransforms
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