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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)

Lecture 16 - Laplace Transform Method for Solving Ordinary Differential Equations


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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