Applied Partial Differential Equations

J. David Logan (Autor)

Buch | Softcover

XI, 289 Seiten

2014 | 3rd ed. 2015
Springer International Publishing (Verlag)
978-3-319-30769-5 (ISBN)

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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 sciences. The topics include derivations of some of the standard models of mathematical physics and methods for solving those equations on unbounded and bounded domains, and applications of PDE's to biology. The text differs from other texts in its brevity; 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.

For the 3rd edition the section on numerical methods has been considerably expanded to reflect their central role in PDE's. A treatment of the finite element method has been included and the code for numerical calculations is now written for MATLAB. Nonetheless the brevity of the text has been maintained. To further aid the reader in mastering the material and using the book, the clarity of the exercises has been improved, more routine exercises have been included, and the entire text has been visually reformatted to improve readability.

lt;br />J. David Logan is Willa Cather Professor of Mathematics at the University of Nebraska Lincoln. He received his PhD from The Ohio State University and has served on the faculties at the University of Arizona, Kansas State University, and Rensselaer Polytechnic Institute. For many years he served as a visiting scientist at Los Alamos and Lawrence Livermore National Laboratories. He has published widely in differential equations, mathematical physics, fluid and gas dynamics, hydrogeology, and mathematical biology. Dr. Logan has authored 7 books, among them A First Course in Differential Equations, 2nd ed., published by Springer.

Preface to the Third Edition.- To the Students.- 1: The Physical Origins of Partial Differential Equations.- 1.1 PDE Models.- 1.2 Conservation Laws.- 1.3 Diffusion.- 1.4 Diffusion and Randomness.- 1.5 Vibrations and Acoustics.- 1.6 Quantum Mechanics*.- 1.7 Heat Conduction in Higher Dimensions.- 1.8 Laplace's Equation.- 1.9 Classification of PDEs.- 2. Partial Differential Equations on Unbounded Domains.- 2.1 Cauchy Problem for the Heat Equation.- 2.2 Cauchy Problem for the Wave Equation.- 2.3 Well-Posed Problems.- 2.4 Semi-Infinite Domains.- 2.5 Sources and Duhamel's Principle.- 2.6 Laplace Transforms.- 2.7 Fourier Transforms.- 3. Orthogonal Expansions.- 3.1 The Fourier Method.- 3.2 Orthogonal Expansions.- 3.3 Classical Fourier Series.-4. Partial Differential Equations on Bounded Domains.- 4.1 Overview of Separation of Variables.- 4.2 Sturm-Liouville Problems - 4.3 Generalization and Singular Problems.- 4.4 Laplace's Equation.- 4.5 Cooling of a Sphere.- 4.6 Diffusion inb a Disk.- 4.7 Sources on Bounded Domains.- 4.8 Poisson's Equation*.-5. Applications in the Life Sciences.-5.1 Age-Structured Models.- 5.2 Traveling Waves Fronts.- 5.3 Equilibria and Stability.- References.- Appendix A. Ordinary Differential Equations.- Index.

"The aim of this book is to provide the reader with basic ideas encountered in partial differential equations. ... The mathematical content is highly motivated by physical problems and the emphasis is on motivation, methods, concepts and interpretation rather than formal theory. The textbook is a valuable material for undergraduate science and engineering students." (Marius Ghergu, zbMATH 1310.35001, 2015)

Erscheinungsdatum	04.02.2016
Reihe/Serie	Undergraduate Texts in Mathematics
Zusatzinfo	XI, 289 p. 51 illus., 6 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	753 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Biologie ► Ökologie / Naturschutz
	Naturwissenschaften ► Biologie ► Zoologie
	Naturwissenschaften ► Physik / Astronomie
Schlagworte	applied PDE text • Community & Population Ecology • Community & Population Ecology • Crank-Nicolson scheme • d'Alembert's formula • Fick's Law • Fourier method • Fourier series • Gauss-Seidel method • Green's identity • Lagrange identity • Laplace transform • Leibniz rule • Mathematical methods in physics • mathematics and statistics • McKendrick-von Forester equation • orthogonal expansion • Partial differential equations • PDE textbook adoption • Sturm-Liouville problem • von Neumann stability analysis
ISBN-10	3-319-30769-X / 331930769X
ISBN-13	978-3-319-30769-5 / 9783319307695
Zustand	Neuware