Media Storage Type : 64 GB USB Stick (2 Nos.)
NPTEL Subject Matter Expert : Prof. Srinivasa Manam
NPTEL Co-ordinating Institute : IIT Madras
NPTEL Lecture Count : 48
NPTEL Course Size : 72 GB
NPTEL PDF Text Transcription : Not Available
NPTEL Subtitle Transcription : Not Available
Lecture Titles:
Lecture 1 - Introduction to Fourier series
Lecture 2 - Fourier series - ExamplesÂ
Lecture 3 - Complex Fourier seriesÂ
Lecture 4 - Conditions for the Convergence of Fourier SeriesÂ
Lecture 5 - Conditions for the Convergence of Fourier Series (Continued...)
Lecture 6 - Use of Delta function in the Fourier series convergence
Lecture 7 - More Examples on Fourier Series of a Periodic Signal
Lecture 8 - Gibb's Phenomenon in the Computation of Fourier Series
Lecture 9 - Properties of Fourier Transform of a Periodic Signal
Lecture 10 - Properties of Fourier transform (Continued...)
Lecture 11 - Parseval's Identity and Recap of Fourier series
Lecture 12 - Fourier integral theorem-an informal proof
Lecture 13 - Definition of Fourier transforms
Lecture 14 - Fourier transform of a Heavyside function
Lecture 15 - Use of Fourier transforms to evaluate some integrals
Lecture 16 - Evaluation of an integral- Recall of complex function theory
Lecture 17 - Properties of Fourier transforms of non-periodic signals
Lecture 18 - More properties of Fourier transforms
Lecture 19 - Fourier integral theorem - proof
Lecture 20 - Application of Fourier transform to ODE's
Lecture 21 - Application of Fourier transforms to differential and integral equations
Lecture 22 - Evaluation of integrals by Fourier transforms
Lecture 23 - D'Alembert's solution by Fourier transform
Lecture 24 - Solution of Heat equation by Fourier transform
Lecture 25 - Solution of Heat and Laplace equations by Fourier transform
Lecture 26 - Introduction to Laplace transform
Lecture 27 - Laplace transform of elementary functions
Lecture 28 - Properties of Laplace transforms
Lecture 29 - Properties of Laplace transforms (Continued...)
Lecture 30 - Methods of finding inverse Laplace transform
Lecture 31 - Heavyside expansion theorem
Lecture 32 - Review of complex function theory
Lecture 33 - Inverse Laplace transform by contour integration
Lecture 34 - Application of Laplace transforms - ODEs'
Lecture 35 - Solutions of initial or boundary value problems for ODEs'
Lecture 36 - Solving first order PDE's by Laplace transform
Lecture 37 - Solution of wave equation by Laplace transform
Lecture 38 - Solving hyperbolic equations by Laplace transform
Lecture 39 - Solving heat equation by Laplace transform
Lecture 40 - Initial boundary value problems for heat equations
Lecture 41 - Solution of Integral Equations by Laplace Transform
Lecture 42 - Evaluation of Integrals by Laplace Transform
Lecture 43 - Introduction to Z-Transforms
Lecture 44 - Properties of Z-Transforms
Lecture 45 - Inverse Z-transforms
Lecture 46 - Solution of difference equations by Z-transforms
Lecture 47 - Evaluation of infinite sums by Z-transforms
Lecture 48 - conclusions