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Mathematics
Partial Differential Equations (Web)
Syllabus
Co-ordinated by :
IIT Guwahati
Available from :
2013-07-04
Lec :
1
Modules / Lectures
Mathematical Preliminaries
A Review of Multivariable Calulus
Essential Ordinary Differential Equations
Surfaces and Integral Curves
Solving Equations dx/P = dy/Q = dz/R
First-Order Partial Differential Equations
First-Order Partial Differential Equations
Linear First-Order PDEs
Quasilinear First-Order PDEs
Nonlinear First-Order PDEs
Compatible Systems and Charpit’s Method
Some Special Types of First-Order PDEs
Jacobi Method for Nonlinear First-Order PDEs
Second-Order Partial Differential Equations
Classification of Second-Order PDEs
Canonical Forms or Normal Forms
Superposition Principle and Wellposedness
Fourier Series
Introduction to Fourier Series
Convergence of Fourier Series
Fourier Cosine and Sine Series
Heat Equation
Modeling the Heat Equation
The Maximum and Minimum Principle
Method of Separation of Variables
Time-Independent Homogeneous BC
Time-Dependent BC
The Wave Equation
Mathematical Formulation and Uniqueness Result
The Infinite String Problem
The Semi-Infinite String Problem
The Finite Vibrating String Problem
The Inhomogeneous Wave Equation
The Laplace Equation
Basic Concepts and The Maximum/Minimum Principle
Green’s Identity and Fundamental Solutions
The Dirichlet BVP for a Rectangle
The Mixed BVP for a Rectangle
The Dirichlet Problems for Annuli
The Dirichlet Problem for the Disk
The Fourier Transform Methdos for PDEs
Fourier Transform
Fourier Sine and Cosine Transformations
Heat Flow Problems
Vibration of an Infinite String
Laplace’s Equation in a Half-Plane
The Method of Green’s Functions
The Laplace Equation
The Wave Equation
The Heat Equation
Bibliography
Bibliography
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