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Course11110213332 lectures

Introduction to Methods of Applied Mathematics

Prof. Mani Mehra and Prof. Vivek Kumar Aggarwal · IIT Delhi

Start with lecture 1 At NPTEL

About

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.

INTENTED AUDIENCE : Any Interested Learners

PREREQUISITES : Some basic knowledge of Calculus, Differential Equations, Topics related to Mathematics – I, II will be an advantage.

Lectures

Week 1

  1. Introduction to First Order Differential Equations YouTube
  2. Introduction to First Order Differential Equations (contd…) YouTube
  3. Introduction to Second Order Linear Differential Equations YouTube

Week 2

  1. Second Order Linear Differential Equations With Constant Coefficients YouTube
  2. Second Order Linear Differential Equations With Constant Coefficients (Contd…) YouTube
  3. Second Order Linear Differential Equations With Variable Coefficients YouTube

Week 3

  1. Factorization of Second order Differential Operator & Euler Cauchy Equation YouTube
  2. Power Series Solution of General Differential Equation YouTube
  3. Green's function YouTube

Week 4

  1. Method of Green's Function for Solving Initial Value & Boundary Value Problems YouTube
  2. Adjoint Linear Differential Operator YouTube
  3. Adjoint Linear Differential Operator (Contd..) YouTube

Week 5

  1. Sturm-Liouvile Problems YouTube
  2. Laplace transformation YouTube
  3. Laplace transformation (Contd…) YouTube

Week 6

  1. Laplace Transform Method for Solving Ordinary Differential Equations YouTube
  2. Laplace Transform Applied to Differential Equations & Convolution YouTube
  3. Fourier Series YouTube

Week 7

  1. Fourier Series (Contd…) YouTube
  2. Gibbs Phenomenon and Parseval's Identity YouTube
  3. Fourier Integral and Fourier Transform YouTube

Week 8

  1. Fourier Integral and Fourier Transform (Contd..) YouTube
  2. Fourier Transform Method for Solving Ordinary Differential Equations YouTube
  3. Frames, Riesz Bases and Orthonormal Bases YouTube

Week 9

  1. Frames, Riesz Bases and Orthonormal Bases (Contd..) YouTube
  2. Fourier Series and Fourier Transform YouTube

Week 10

  1. Time-Frequency Analysis and Gabor Transform YouTube
  2. Window Fourier Transform and Multiresolution Analysis YouTube

Week 11

  1. Construction of Scaling Functions and Wavelets Using Multiresolution Analysis YouTube
  2. Daubechies Wavelet YouTube

Week 12

  1. Daubechies Wavelet (Contd…) YouTube
  2. Wavelet Transform and Shannon Wavelet YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Delhi
Department
Mathematics
Taught by
Prof. Mani Mehra, Prof. Vivek Kumar Aggarwal
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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