Applied Partial Differential Equations

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Springer Science & Business Media, Jun 18, 2004 - Mathematics - 209 pages
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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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Contents

The Physical Origins of Partial Differential Equations
ix
12 Conservation Laws
5
13 Diffusion
12
14 PDE Models in Biology
18
15 Vibrations and Acoustics
28
16 Quantum Mechanics
35
17 Heat Flow in Three Dimensions
38
18 Laplaces Equation
43
33 Classical Fourier Series
103
34 SturmLiouville Problems
108
Partial Differential Equations on Bounded Domains
117
42 Flux and Radiation Conditions
125
43 Laplaces Equation
132
44 Cooling of a Sphere
139
45 Diffusion in a Disk
144
46 Sources on Bounded Domains
148

19 Classification of PDEs
48
Partial Differential Equations on Unbounded Domains
54
22 Cauchy Problem for the Wave Equation
60
23 IllPosed Problems
65
24 SemiInfinite Domains
68
25 Sources and Duhamels Principle
72
26 Laplace Transforms
77
27 Fourier Transforms
82
28 Solving PDEs Using Computer Algebra Systems
88
Orthogonal Expansions
92
32 Orthogonal Expansions
94
47 Parameter Identification Problems
152
48 Finite Difference Methods
157
Partial Differential Equations in the Life Sciences
168
52 Traveling Waves Fronts
177
53 Equilibria and Stability
183
Ordinary Differential Equations
193
TABLE OF LAPLACE TRANSFORMS
199
References
201
Index
203
Copyright

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About the author (2004)

J. David Logan is Professor of Mathematics at University of Nebraska, Lincoln.

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