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Solution techniques for elementary partial differential equations


Solution techniques for elementary partial differential equations

Title: Solution techniques for elementary partial differential equations | Author(s): Constanda C. | Publisher: CRC Press | Year: 2010 | Edition: 2 | Language: English | Pages : 340 | ISBN: 9781439811405 | Size: 2 MB  | Extension: pdf

 

Features

  • Gives students the necessary theoretical foundation and practical experience for solving analytical problems
  • Presents a variety of solution methods, including the separation of variables, eigenfunction expansion, Fourier and Laplace transformations, Green’s functions, and asymptotic techniques
  • Includes Mathematica® code that enables students to check the accuracy of their work without interfering with the solution procedure
  • Contains a wealth of worked examples and exercises—both computational exercises and standard problems not requiring a software package

A solutions manual and PDF projector files are available upon qualifying course adoption.

Summary

Solution Techniques for Elementary Partial Differential Equations, Third Edition remains a top choice for a standard, undergraduate-level course on partial differential equations (PDEs). Making the text even more user-friendly, this third edition covers important and widely used methods for solving PDEs.

New to the Third Edition

  • New sections on the series expansion of more general functions, other problems of general second-order linear equations, vibrating string with other types of boundary conditions, and equilibrium temperature in an infinite strip
  • Reorganized sections that make it easier for students and professors to navigate the contents
  • Rearranged exercises that are now at the end of each section/subsection instead of at the end of the chapter
  • New and improved exercises and worked examples
  • A brief Mathematica® program for nearly all of the worked examples, showing students how to verify results by computer

 

This bestselling, highly praised textbook uses a streamlined, direct approach to develop students’ competence in solving PDEs. It offers concise, easily understood explanations and worked examples that allow students to see the techniques in action.

 

Table of Contents

Ordinary Differential Equations: Brief Revision
First-Order Equations

Homogeneous Linear Equations with Constant Coefficients
Nonhomogeneous Linear Equations with Constant Coefficients
Cauchy–Euler Equations
Functions and Operators

 

Fourier Series
The Full Fourier Series

Fourier Sine and Cosine Series
Convergence and Differentiation
Series Expansion of More General Functions

 

Sturm–Liouville Problems
Regular Sturm–Liouville Problems

Other Problems
Bessel Functions
Legendre Polynomials
Spherical Harmonics

 

Some Fundamental Equations of Mathematical Physics
The Heat Equation

The Laplace Equation
The Wave Equation
Other Equations

 

The Method of Separation of Variables
The Heat Equation

The Wave Equation
The Laplace Equation
Other Equations
Equations with More Than Two Variables

 

Linear Nonhomogeneous Problems
Equilibrium Solutions

Nonhomogeneous Problems

 

The Method of Eigenfunction Expansion
The Nonhomogeneous Heat Equation

The Nonhomogeneous Wave Equation
The Nonhomogeneous Laplace Equation
Other Nonhomogeneous Equations

 

The Fourier Transformations
The Full Fourier Transformation

The Fourier Sine and Cosine Transformations
Other Applications

 

The Laplace Transformation
Definition and Properties

Applications

 

The Method of Green’s Functions
The Heat Equation
The Laplace Equation
The Wave Equation

 

General Second-Order Linear Equations
The Canonical Form

Hyperbolic Equations
Parabolic Equations
Elliptic Equations
Other Problems

 

The Method of Characteristics
First-Order Linear Equations

First-Order Quasilinear Equations
The One-Dimensional Wave Equation
Other Hyperbolic Equations

 

Perturbation and Asymptotic Methods
Asymptotic Series

Regular Perturbation Problems
Singular Perturbation Problems

 

Complex Variable Methods
Elliptic Equations
Systems of Equations

 

Appendix

Further Reading

Index


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