Partial Differential Equations XCTD6GCJR0
| URI | m2://res/XCTD6GCJR0 |
|---|---|
| Kind | course |
| Creators | Rajen Kumar Sinha (instructor) |
| MSC | 35-XX |
| Scope | in |
| Ids | course 0022nd079:111103021 |
Expressions
e1: edition
| Language | en |
|---|
- m1: page, IIT Guwahati (record). nptel 111103021
Contents
- part 1: Mathematical Preliminaries
- session 1: A Review of Multivariable Calulus
- session 2: Essential Ordinary Differential Equations
- session 3: Surfaces and Integral Curves
- session 4: Solving Equations dx/P = dy/Q = dz/R
- part 2: First-Order Partial Differential Equations
- session 5: First-Order Partial Differential Equations
- session 6: Linear First-Order PDEs
- session 7: Quasilinear First-Order PDEs
- session 8: Nonlinear First-Order PDEs
- session 9: Compatible Systems and Charpit’s Method
- session 10: Some Special Types of First-Order PDEs
- session 11: Jacobi Method for Nonlinear First-Order PDEs
- part 3: Second-Order Partial Differential Equations
- session 12: Classification of Second-Order PDEs
- session 13: Canonical Forms or Normal Forms
- session 14: Superposition Principle and Wellposedness
- part 4: Fourier Series
- session 15: Introduction to Fourier Series
- session 16: Convergence of Fourier Series
- session 17: Fourier Cosine and Sine Series
- part 5: Heat Equation
- session 18: Modeling the Heat Equation
- session 19: The Maximum and Minimum Principle
- session 20: Method of Separation of Variables
- session 21: Time-Independent Homogeneous BC
- session 22: Time-Dependent BC
- part 6: The Wave Equation
- session 23: Mathematical Formulation and Uniqueness Result
- session 24: The Infinite String Problem
- session 25: The Semi-Infinite String Problem
- session 26: The Finite Vibrating String Problem
- session 27: The Inhomogeneous Wave Equation
- part 7: The Laplace Equation
- session 28: Basic Concepts and The Maximum/Minimum Principle
- session 29: Green’s Identity and Fundamental Solutions
- session 30: The Dirichlet BVP for a Rectangle
- session 31: The Mixed BVP for a Rectangle
- session 32: The Dirichlet Problems for Annuli
- session 33: The Dirichlet Problem for the Disk
- part 8: The Fourier Transform Methdos for PDEs
- session 34: Fourier Transform
- session 35: Fourier Sine and Cosine Transformations
- session 36: Heat Flow Problems
- session 37: Vibration of an Infinite String
- session 38: Laplace’s Equation in a Half-Plane
- part 9: The Method of Green’s Functions
- session 39: The Laplace Equation
- session 40: The Wave Equation
- session 41: The Heat Equation
- part 10: Bibliography
- session 42: Bibliography
Catalogue records
- nptel: 111103021 (manifestation)