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ISBN13: 978-0471238874

ISBN10: 0471238872

Edition: 99

Copyright: 1999

Publisher: John Wiley & Sons, Inc.

Published: 1999

International: No

ISBN10: 0471238872

Edition: 99

Copyright: 1999

Publisher: John Wiley & Sons, Inc.

Published: 1999

International: No

Beginning Partial Differential Equations provides a challenging yet accessible introduction to partial differential equations for advanced undergraduate and beginning graduate students. Features include:

* A discussion of first order equations and the method of characteristics for quasi-linear first order PDEs

* Canonical forms of second order PDEs

* Characteristics and the Cauchy problem

* A proof of the Cauchy-Kowalevski theorem for linear systems

* A self-contained development of tools from Fourier analysis

* Connections between the mathematics and physical interpretations of PDEs

* Numerous exercises, many with solutions provided

* Experimental, computer-based exercises designed to develop lines of inquiry.

The treatment of second order PDEs focuses on well-posed problems, properties and behavior of solutions, existence and uniqueness of solutions, and techniques for writing representations of solutions. Techniques include the use of characteristics, Fourier methods, and, for the Dirichlet problem, Green's function and conformal mappings. Also included are the Kirchhoff/Poisson solution of the wave equation, Huygens's principle, and Lebesgue's example of a Dirichlet problem with no solution.

**Features:**

- Emphasizes the structural aspects of partiallydifferential equations, using the geometry of characteristicsas a starting point
- · Introduces theory at an introductory level,backed by excellent explanations of techniques and numerous practicalexamples
- The exercises serve two purposes: Some are computational,ranging from routine to challenging with answers to many of thequestions included in the back of the book. Other exercises provideadditional information regarding partial differential equations. For these, the title includes hints for the development of aproof or derivation.
- Problems are based on physical phenomena suchas the effects of density on the vibrations of a guitar string. Sections of the problems invite graphic representation and computationalpackages as MAPLE® or MATHEMATICA® can be used to enhancethese exercises
- · Provides students with a sound foundationin partial differential equations· Fills a niche in the world of mathematicsby serving as a bridge to higher concepts· Does not assume the reader possesses knowledgeof Fourier Analysis and incorporates descriptions of the techniqueinto its text

Author Bio

**O'Neil, Peter V. : University of Alabama**

Peter V. O'Neil is Provost at the University of Alabama at Birmingham. His books include Advanced Engineering Mathematics, Fourth Edition.

First Order Partial Differential Equations.

Linear Second Order Partial Differential Equations.

Elements of Fourier Analysis.

The Wave Equation.

The Heat Equation.

Dirichlet and Neumann Problems.

Conclusion.

Index.

ISBN10: 0471238872

Edition: 99

Copyright: 1999

Publisher: John Wiley & Sons, Inc.

Published: 1999

International: No

Beginning Partial Differential Equations provides a challenging yet accessible introduction to partial differential equations for advanced undergraduate and beginning graduate students. Features include:

* A discussion of first order equations and the method of characteristics for quasi-linear first order PDEs

* Canonical forms of second order PDEs

* Characteristics and the Cauchy problem

* A proof of the Cauchy-Kowalevski theorem for linear systems

* A self-contained development of tools from Fourier analysis

* Connections between the mathematics and physical interpretations of PDEs

* Numerous exercises, many with solutions provided

* Experimental, computer-based exercises designed to develop lines of inquiry.

The treatment of second order PDEs focuses on well-posed problems, properties and behavior of solutions, existence and uniqueness of solutions, and techniques for writing representations of solutions. Techniques include the use of characteristics, Fourier methods, and, for the Dirichlet problem, Green's function and conformal mappings. Also included are the Kirchhoff/Poisson solution of the wave equation, Huygens's principle, and Lebesgue's example of a Dirichlet problem with no solution.

**Features:**

- Emphasizes the structural aspects of partiallydifferential equations, using the geometry of characteristicsas a starting point
- · Introduces theory at an introductory level,backed by excellent explanations of techniques and numerous practicalexamples
- The exercises serve two purposes: Some are computational,ranging from routine to challenging with answers to many of thequestions included in the back of the book. Other exercises provideadditional information regarding partial differential equations. For these, the title includes hints for the development of aproof or derivation.
- Problems are based on physical phenomena suchas the effects of density on the vibrations of a guitar string. Sections of the problems invite graphic representation and computationalpackages as MAPLE® or MATHEMATICA® can be used to enhancethese exercises
- · Provides students with a sound foundationin partial differential equations· Fills a niche in the world of mathematicsby serving as a bridge to higher concepts· Does not assume the reader possesses knowledgeof Fourier Analysis and incorporates descriptions of the techniqueinto its text

Author Bio

**O'Neil, Peter V. : University of Alabama**

Peter V. O'Neil is Provost at the University of Alabama at Birmingham. His books include Advanced Engineering Mathematics, Fourth Edition.

Table of Contents

Linear Second Order Partial Differential Equations.

Elements of Fourier Analysis.

The Wave Equation.

The Heat Equation.

Dirichlet and Neumann Problems.

Conclusion.

Index.

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