Learn · Transform Techniques for Engineers
Lecture 16 of 47Week 4
Evaluation of an integral- Recall of complex function theory
Prof. Srinivasa Rao Manam · IIT Madras
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- Transform Techniques for Engineers, IIT Madras (at NPTEL)
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- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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All the lectures
- Introduction to Fourier series
- Fourier series - Examples
- Complex Fourier series
- Conditions for the Convergence of Fourier Series
- Conditions for the Convergence of Fourier Series(continued)
- Use of Delta function in the Fourier series convergence
- 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
- 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
- Inverse Z-transforms
- Solution of difference equations by Z-transforms
- Evaluation of infinite sums by Z-transforms
- conclusions