# Applied Partial Differential Equations

Springer, Jun 18, 2004 - Mathematics - 209 pages

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

### References from web pages

University of Western Ontario Applied Mathematics 315a Partial ...
Applied Partial Differential Equations by Logan, J. David. Series: Undergraduate Texts in Mathematics, 2nd ed., 2004, XII, 212 p. 40 illus., Soft-cover, ...
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livre 2 ordm cycle et maths appliquees a la physique : this textbook is for the standard, one-semester, junior-senior course that often goes by the title ...
www.lavoisier.fr/ notice/ fr408073.html

JSTOR: Featured Review: PDE Books, Present and Future
Applied Partial Differential Equations. By J. Ockendon, S. Howison, ..... [6] P. DUCHATEAU AND D. ZACHMANN, Applied Partial Differential Equations, ...

SFU Math 418-3: pdes, Fall 2002
R. Haberman, Elementary Applied Partial Differential Equations : with Fourier ... jd Logan, Applied Partial Differential Equations, Springer-Verlag (1998). ...
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Syllabus for MATH 603 Title : Methods of Applied Mathematics II ...
J. David Logan, Applied Partial Differential Equations, Springer, 1988. Peter V. O'Neil,. Beginning Partial Differential Equations, Wiley, X999. ...

Lehrbüchersammlung
jd Logan (2004), Applied Partial Differential Equations, Springer Berlin, (0-387-20935-2). kk Sobczyk, dj (2001), Stochastic Modeling of Microstructures,
www.asim-gi.org/ index.php?id=260