Introduction to Partial Differential Equations 1st Edition by Rao KS ISBN 8120342224 9788120342224

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ISBN 10: 8120342224 
ISBN 13: 9788120342224
Author: Rao KS

This textbook is an introduction to the methods needed to solve partial differential equations (PDEs). Readers are introduced to PDEs that come from a variety of fields in engineering and the natural sciences. The chapters include the following topics:  First Order PDEs, Second Order PDEs, Fourier Series, Separation of Variables, the Fourier Transform, and higher dimensional problems. Readers are guided through these chapters where techniques for solving first and second order PDEs are introduced. Each chapter ends with series of exercises to facilitate learning as well as illustrate the material presented in each chapter. 

Introduction to Partial Differential Equations 1st Table of contents:

• Introduction

  • What Are Partial Differential Equations?

  • Classification of PDEs

  • Examples from Physics and Engineering

• First-Order Partial Differential Equations

  • Method of Characteristics

  • Linear and Nonlinear First-Order Equations

  • Applications

• Second-Order PDEs: Classification and Canonical Forms

  • Elliptic, Parabolic, and Hyperbolic Equations

  • Change of Variables

  • Canonical Forms

• The Heat Equation

  • Derivation and Physical Interpretation

  • Initial and Boundary Value Problems

  • Separation of Variables

• The Wave Equation

  • Derivation and Physical Meaning

  • Solution Techniques

  • D’Alembert’s Formula

• Laplace’s Equation and Harmonic Functions

  • Boundary Value Problems

  • Maximum Principle

  • Mean Value Property

• Fourier Series and Eigenvalue Problems

  • Orthogonality and Completeness

  • Sturm-Liouville Theory

  • Applications to PDEs

• Green’s Functions and Integral Methods

  • Construction of Green’s Functions

  • Representation of Solutions

  • Applications

• Numerical Methods for PDEs

  • Finite Difference Methods

  • Stability and Convergence

  • Examples

• Nonlinear PDEs and Further Topics

  • Introduction to Nonlinear Problems

  • Shock Waves and Conservation Laws

  • Other Advanced Topics

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Tags: Rao KS, Partial Differential