Applied Partial Differential Equations / Edition 2

Applied Partial Differential Equations / Edition 2

by J. David Logan
     
 

ISBN-10: 0387209352

ISBN-13: 9780387209357

Pub. Date: 06/25/2010

Publisher: Springer New York

This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems". The audience consists of students in mathematics, engineering, and the physical sciences. The topics include derivations of some of the standard models of mathematical physics (e.g., the heat

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Overview

This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems". The audience consists of students in mathematics, engineering, and the physical sciences. The topics include derivations of some of the standard models of mathematical physics (e.g., the heat equation, the wave equation, and Laplace’s equation) and methods for solving those equations on unbounded and bounded domains (transform methods and eigenfunction expansions). Prerequisites include multivariable calculus and elementary differential equations. The text differs from other texts in that it is a brief treatment; yet it provides coverage of the main topics usually studied in the standard course as well as an introduction to using computer algebra packages to solve and understand partial differential equations. The many exercises help students sharpen their computational skills by encouraging them to think about concepts and derivations. The student who reads this book carefully and solves most of the problems will have a sound knowledge base for a second-year partial differential equations course where careful proofs are constructed or for upper division courses in science and engineering where detailed applications of partial differential equations are introduced.

To give this text an even wider appeal, the second edition has been updated with a new chapter on partial differential equation models in biology, and with various examples from the life sciences that have been added throughout the text. There are more exercises, as well as solutions and hints to some of the problems at the end of the book.

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Product Details

ISBN-13:
9780387209357
Publisher:
Springer New York
Publication date:
06/25/2010
Series:
Undergraduate Texts in Mathematics Series
Edition description:
2nd ed. 2004
Pages:
212
Product dimensions:
0.56(w) x 9.21(h) x 6.14(d)

Table of Contents

Ch. 1The physical origins of partial differential1
1.1Mathematical models1
1.2Conservation laws9
1.3Diffusion16
1.4PDEs in biology22
1.5Vibrations and acoustics32
1.6Quantum mechanics39
1.7Heat flow in three dimensions42
1.8Laplace's equation47
1.9Classification of PDEs52
Ch. 2Partial differential equations on unbounded domains58
2.1Cauchy problem for the heat equation58
2.2Cauchy problem for the wave equation64
2.3Ill-posed problems69
2.4Semi-infinite domains72
2.5Sources and Duhamel's principle76

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