Introduction to Methods of Applied Mathematics (Prof. Vivek Kumar Aggarwal, IIT Delhi) | Mathematics

Introduction to Methods of Applied Mathematics

Introduction to Methods of Applied Mathematics. Instructors: Prof. Vivek Kumar Aggarwal and Prof. Mani Mehra, Department of Mathematics, IIT Delhi. This course is aimed at final year undergraduate and graduate students in engineering, physics and applied mathematics. This will cover the very important and essential topics used by almost all branches of Science and engineering. (from nptel.ac.in)

Introduction

Lecture 01 - Introduction to First Order Differential Equations

Lecture 02 - Introduction to First Order Differential Equations (cont.)

Lecture 03 - Introduction to Second Order Linear Differential Equations

Lecture 04 - Second Order Linear Differential Equations with Constant Coefficients

Lecture 05 - Second Order Linear Differential Equations with Constant Coefficients (cont.)

Lecture 06 - Second Order Linear Differential Equations with Variable Coefficients

Lecture 07 - Factorization of Second Order Differential Operator and Euler-Cauchy Equation

Lecture 08 - Power Series Solution of General Differential Equation

Lecture 09 - Green's Function

Lecture 10 - Method of Green's Function for Solving Initial Value and Boundary Value Problems

Lecture 11 - Adjoint Linear Differential Operator

Lecture 12 - Adjoint Linear Differential Operator (cont.)

Lecture 13 - Sturm-Liouville Problems

Lecture 14 - Laplace Transformation

Lecture 15 - Laplace Transformation (cont.)

Lecture 16 - Laplace Transform Method for Solving Ordinary Differential Equations

Lecture 17 - Laplace Transform Applied to Differential Equations and Convolution

Lecture 18 - Fourier Series

Lecture 19 - Fourier Series (cont.)

Lecture 20 - Gibbs Phenomenon and Parseval's Identity

Lecture 21 - Fourier Integral and Fourier Transform

Lecture 22 - Fourier Integral and Fourier Transform (cont.)

Lecture 23 - Fourier Transform Method for Solving Ordinary Differential Equations

Lecture 24 - Frames, Riesz Bases and Orthonormal Bases

Lecture 25 - Frames, Riesz Bases and Orthonormal Bases (cont.)

Lecture 26 - Fourier Series and Fourier Transform

Lecture 27 - Time-Frequency Analysis and Gabor Transform

Lecture 28 - Window Fourier Transform and Multiresolution Analysis

Lecture 29 - Construction of Scaling Functions and Wavelets Using Multiresolution Analysis

Lecture 30 - Daubechies Wavelet

Lecture 31 - Daubechies Wavelet (cont.)

Lecture 32 - Wavelet Transform and Shannon Wavelet

References

Introduction to Methods of Applied Mathematics
Instructors: Prof. Vivek Kumar Aggarwal and Prof. Mani Mehra, Department of Mathematics, IIT Delhi. This course is aimed at final year undergraduate and graduate students in engineering, physics and applied mathematics.