Integral Transforms and their Applications
Integral Transforms and their Applications. Instructor: Prof. Sarthok Sircar, Department of Mathematics, IIT Delhi. The course is designed as an introduction to the theory and applications of integral transforms to problems in linear differential equations, to boundary and initial value problems in partial differential equations and continuum mechanics. Many new applications in applied mathematics, physics, chemistry, biology and engineering are included. This course will serve as a reference for advanced study and research in this subject as well as for its applications in the fields of signal processing, informatics and communications, neuroscience, fluid mechanics, quantum mechanics, computer assisted tomography (CAT). The course is open to all MTech, PhD students, some final year advanced undergraduate and honors students.
(from nptel.ac.in)
| Lecture 01 - Introduction to Fourier Transforms, Part 1 |
| Lecture 02 - Introduction to Fourier Transforms, Part 2 |
| Lecture 03 - Introduction to Fourier Transforms, Part 3 |
| Lecture 04 - Properties of Fourier Transforms, Shannon Sampling Theorem, Gibbs Phenomena, Part 1 |
| Lecture 05 - Properties of Fourier Transforms, Shannon Sampling Theorem, Gibbs Phenomena, Part 2 |
| Lecture 06 - Properties of Fourier Transforms, Shannon Sampling Theorem, Gibbs Phenomena, Part 3 |
| Lecture 07 - Applications of Fourier Transforms, Part 1 |
| Lecture 08 - Applications of Fourier Transforms, Part 2 |
| Lecture 09 - Applications of Fourier Transforms, Part 3 |
| Lecture 10 - Introduction to Laplace Transforms, Part 1 |
| Lecture 11 - Introduction to Laplace Transforms, Part 2 |
| Lecture 12 - Introduction to Laplace Transforms, Part 3 |
| Lecture 13 - Inverse Laplace Transforms, Initial and Final Value Theorems, Part 1 |
| Lecture 14 - Inverse Laplace Transforms, Initial and Final Value Theorems, Part 2 |
| Lecture 15 - Inverse Laplace Transforms, Initial and Final Value Theorems, Part 3 |
| Lecture 16 - Applications of Laplace Transforms, Part 1 |
| Lecture 17 - Applications of Laplace Transforms, Part 2 |
| Lecture 18 - Applications of Laplace Transforms, Part 3 |
| Lecture 19 - Applications of Laplace Transforms (cont.), Part 1 |
| Lecture 20 - Applications of Laplace Transforms (cont.), Part 2 |
| Lecture 21 - Applications of Laplace Transforms (cont.), Part 3 |
| Lecture 22 - Applications of Fourier-Laplace Transforms, Part 1 |
| Lecture 23 - Applications of Fourier-Laplace Transforms, Part 2 |
| Lecture 24 - Applications of Fourier-Laplace Transforms, Part 3 |
| Lecture 25 - Introduction to Hankel Transforms, Part 1 |
| Lecture 26 - Introduction to Hankel Transforms, Part 2 |
| Lecture 27 - Introduction to Hankel Transforms, Part 3 |
| Lecture 28 - Introduction to Mellin Transforms, Part 1 |
| Lecture 29 - Introduction to Mellin Transforms, Part 2 |
| Lecture 30 - Introduction to Mellin Transforms, Part 3 |
| Lecture 31 - Introduction to Hilbert Transforms, Part 1 |
| Lecture 32 - Introduction to Hilbert Transforms, Part 2 |
| Lecture 33 - Introduction to Hilbert Transforms, Part 3 |
| Lecture 34 - Applications of Hilbert Transforms, Introduction to Stieltjes Transform, Part 1 |
| Lecture 35 - Applications of Hilbert Transforms, Introduction to Stieltjes Transform, Part 2 |
| Lecture 36 - Applications of Hilbert Transforms, Introduction to Stieltjes Transform, Part 3 |
| Lecture 37 - Applications of Stieltjes Transform, Generalized Stieltjes Transform, Part 1 |
| Lecture 38 - Applications of Stieltjes Transform, Generalized Stieltjes Transform, Part 2 |
| Lecture 39 - Applications of Stieltjes Transform, Generalized Stieltjes Transform, Part 3 |
| Lecture 40 - Introduction to Legendre Transform, Part 1 |
| Lecture 41 - Introduction to Legendre Transform, Part 2 |
| Lecture 42 - Introduction to Legendre Transform, Part 3 |
| Lecture 43 - Introduction to z-Transform, Part 1 |
| Lecture 44 - Introduction to z-Transform, Part 2 |
| Lecture 45 - Introduction to z-Transform, Part 3 |
| Lecture 46 - Inverse z-Transform, Applications of z-Transform, Part 1 |
| Lecture 47 - Inverse z-Transform, Applications of z-Transform, Part 2 |
| Lecture 48 - Inverse z-Transform, Applications of z-Transform, Part 3 |
| Lecture 49 - Introduction to Radon Transform, Part 1 |
| Lecture 50 - Introduction to Radon Transform, Part 2 |
| Lecture 51 - Introduction to Radon Transform, Part 3 |
| Lecture 52 - Inverse Radon Transform, Applications to Radon Transform, Part 1 |
| Lecture 53 - Inverse Radon Transform, Applications to Radon Transform, Part 2 |
| Lecture 54 - Inverse Radon Transform, Applications to Radon Transform, Part 3 |
| Lecture 55 - Introduction to Fractional Calculus, Part 1 |
| Lecture 56 - Introduction to Fractional Calculus, Part 2 |
| Lecture 57 - Introduction to Fractional Calculus, Part 3 |
| Lecture 58 - Fractional ODEs, Abel's Integral Equations, Part 1 |
| Lecture 59 - Fractional ODEs, Abel's Integral Equations, Part 2 |
| Lecture 60 - Fractional ODEs, Abel's Integral Equations, Part 3 |
| Lecture 61 - Fractional PDEs, Part 1 |
| Lecture 62 - Fractional PDEs, Part 2 |
| Lecture 63 - Fractional PDEs, Part 3 |
| Lecture 64 - Fractional ODEs and PDEs (cont.), Part 1 |
| Lecture 65 - Fractional ODEs and PDEs (cont.), Part 2 |
| Lecture 66 - Fractional ODEs and PDEs (cont.), Part 3 |
| Lecture 67 - Introduction to Wavelet Transform, Part 1 |
| Lecture 68 - Introduction to Wavelet Transform, Part 2 |
| Lecture 69 - Introduction to Wavelet Transform, Part 3 |
| Lecture 70 - Discrete Haar, Shannon and Daubechies Wavelet, Part 1 |
| Lecture 71 - Discrete Haar, Shannon and Daubechies Wavelet, Part 2 |
| Lecture 72 - Discrete Haar, Shannon and Daubechies Wavelet, Part 3 |
| References |
Integral Transforms and their Applications
Instructor: Prof. Sarthok Sircar, Department of Mathematics, IIT Delhi. The course is designed as an introduction to the theory and applications of integral transforms to problems in linear differential equations, to boundary and initial value problems in partial differential equations and continuum mechanics.
|