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September 23, 2023

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Description

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)

Course Curriculum

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

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