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Mathematics III

Module 1. Instructor: Dr. P. N. Agrawal, Department of Mathematics, IIT Roorkee
Solution of ODE of First Order and First Degree, Linear Differential Equations of the First Order, Approximate Solution of an Initial Value Problem, Series Solution of Homogeneous Linear Differential Equations, Bessel Functions and Their Properties, Laplace Transformation, Applications of Laplace Transformation, One Dimensional Wave Equation, One Dimensional Heat Equation.

Module 2. Instructor: Dr. Tanuja Srivastava, Department of Mathematics, IIT Roorkee
Introduction to Differential Equation, First Order Differential Equations and Their Geometric Interpretation, Differential Equations of First Order and Higher Degree, Linear Differential Equations of Second Order, Euler-Cauchy Theorem, Higher Order Linear Differential Equations, Higher Order Non-homogeneous Linear Equations, Boundary Value Problems, Sturm Liouville Boundary Value Problems, Fourier Series, Convergence of the Fourier Series, Fourier Integrals, Fourier Transforms, Partial Differential Equation, Solution of One Dimensional Wave Equation, Fourier Integral and Transform Method for Heat Equation, Three Dimensional Laplace Equations, Solution of Dirichlet Problem, Numerical Method for Laplace and Poisson Equations.
(from nptel.ac.in)

Solution of ODE of First Order and First Degree


Module 1 by Dr. P. N. Agrawal
Lecture 01 - Solution of ODE of First Order and First Degree
Lecture 02 - Linear Differential Equations of the First Order and Orthogonal Trajectories
Lecture 03 - Approximate Solution of an Initial Value Problem
Lecture 04 - Series Solution of Homogeneous Linear Differential Equations I
Lecture 05 - Series Solution of Homogeneous Linear Differential Equations II
Lecture 06 - Bessel Functions and Their Properties
Lecture 07 - Bessel Functions and Their Properties (cont.)
Lecture 08 - Laplace Transformation
Lecture 09 - Laplace Transformation (cont.)
Lecture 10 - Applications of Laplace Transformation
Lecture 11 - Applications of Laplace Transformation (cont.)
Lecture 12 - One Dimensional Wave Equation
Lecture 13 - One Dimensional Heat Equation
Module 2 by Dr. Tanuja Srivastava
Lecture 14 - Introduction to Differential Equation
Lecture 15 - First Order Differential Equations and Their Geometric Interpretation
Lecture 16 - Differential Equations of First Order and Higher Degree
Lecture 17 - Linear Differential Equations of Second Order - Part 1
Lecture 18 - Linear Differential Equations of Second Order - Part 2
Lecture 19 - Euler-Cauchy Theorem
Lecture 20 - Higher Order Linear Differential Equations
Lecture 21 - Higher Order Non-homogeneous Linear Equations
Lecture 22 - Boundary Value Problems
Lecture 23 - Sturm Liouville Boundary Value Problems
Lecture 24 - Fourier Series - Part 1
Lecture 25 - Fourier Series - Part 2
Lecture 26 - Convergence of the Fourier Series
Lecture 27 - Fourier Integrals
Lecture 28 - Fourier Transforms
Lecture 29 - Partial Differential Equation
Lecture 30 - First Order Partial Differential Equation
Lecture 31 - Second Order Partial Differential Equations - Part I
Lecture 32 - Second Order Partial Differential Equations - Part II
Lecture 33 - Solution of One Dimensional Wave Equation
Lecture 34 - Solution of Homogeneous and Non-homogeneous Equations
Lecture 35 - Fourier Integral and Transform Method for Heat Equation
Lecture 36 - Three Dimensional Laplace Equations
Lecture 37 - Solution of Dirichlet Problem
Lecture 38 - Numerical Method for Laplace and Poisson Equations
Lecture 39 - ADI Method for Laplace and Poisson Equations

References
Mathematics III
Instructors: Dr. P. N. Agrawal and Dr. Tanuja Srivastava, Department of Mathematics, IIT Roorkee. Differential Equations.