Media Storage Type : DVD-ROM
NPTEL Course Name : Partial Differential Equations
NPTEL Subject Matter Expert : Dr. Rajen Kumar Sinha
NPTEL Co-ordinating Institute : IIT Guwahati
NPTEL Lecture Count : 42
Lecture Titles:
Lecture 1 - A Review of Multivariable Calulus
Lecture 2 - Essential Ordinary Differential Equations
Lecture 3 - Surfaces and Integral Curves
Lecture 4 - Solving Equations dx/P = dy/Q = dz/R
Lecture 5 - First-Order Partial Differential Equations
Lecture 6 - Linear First-Order PDEs
Lecture 7 - Quasilinear First-Order PDEs
Lecture 8 - Nonlinear First-Order PDEs
Lecture 9 - Compatible Systems and Charpitï¾’s Method
Lecture 10 - Some Special Types of First-Order PDEs
Lecture 11 - Jacobi Method for Nonlinear First-Order PDEs
Lecture 12 - Classification of Second-Order PDEs
Lecture 13 - Canonical Forms or Normal Forms
Lecture 14 - Superposition Principle and Wellposedness
Lecture 15 - Introduction to Fourier Series
Lecture 16 - Convergence of Fourier Series
Lecture 17 - Fourier Cosine and Sine Series
Lecture 18 - Modeling the Heat Equation
Lecture 19 - The Maximum and Minimum Principle
Lecture 20 - Method of Separation of Variables
Lecture 21 - Time-Independent Homogeneous BC
Lecture 22 - Time-Dependent BC
Lecture 23 - Mathematical Formulation and Uniqueness Result
Lecture 24 - The Infinite String Problem
Lecture 25 - The Semi-Infinite String Problem
Lecture 26 - The Finite Vibrating String Problem
Lecture 27 - The Inhomogeneous Wave Equation
Lecture 28 - Basic Concepts and The Maximum/Minimum Principle
Lecture 29 - Greenï¾’s Identity and Fundamental Solutions
Lecture 30 - The Dirichlet BVP for a Rectangle
Lecture 31 - The Mixed BVP for a Rectangle
Lecture 32 - The Dirichlet Problems for Annuli
Lecture 33 - The Dirichlet Problem for the Disk
Lecture 34 - Fourier Transform
Lecture 35 - Fourier Sine and Cosine Transformations
Lecture 36 - Heat Flow Problems
Lecture 37 - Vibration of an Infinite String
Lecture 38 - Laplaceï¾’s Equation in a Half-Plane
Lecture 39 - The Laplace Equation
Lecture 40 - The Wave Equation
Lecture 41 - The Heat Equation
Lecture 42 - Bibliography