Partial Differential Equations and Boundary-Value Problems with Applications

Inbunden, Engelska, 2011

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Beskrivning

Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.

Produktinformation

Utgivningsdatum:2011-09-30
Vikt:1 120 g
Format:Inbunden
Språk:Engelska
Serie:Pure and Applied Undergraduate Texts
Antal sidor:526
Upplaga:3
Förlag:American Mathematical Society
ISBN:9780821868898

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Mer om författaren

Mark A. Pinsky, Northwestern University, Evanston, IL, USA

Recensioner i media

With more than 200 working examples and 700 exercises (more than 450 with answers) this book is suitable for an undergraduate course in PDEs." - Zentralblatt MATH"I have been one of the cheerleaders for Mark's book PDE and BVP over the years. . . . [M]ost texts for undergraduates are either too advanced or lacking mathematical rigor. Mark's book captures just the right balance. I found [it] easy to use and the problems were doable by my students. His latest edition added some rather important topics that were not covered earlier and emphasized points where the grind it out Fourier methods did not apply." - Marshall Slemrod, University of Wisconsin-Madison, Madison, WI, USA"I have used Partial Differential Equations and Boundary-Value Problems with Applications by Mark Pinsky to teach a one semester undergraduate course on Partial Differential Equations since we first offered the course in 1990. Major strengths [of the book]: The book is very well and concisely written. There is an excellent collection of problems. There is a good appendix with a review of ODE. There is a good appendix on a 'review of infinite series.' There are numerous interesting examples. There is a chapter on asymptomatic analysis. There is a chapter on numerical analysis. . . . Most students have liked the book and I have found it very convenient to teach out of." - Nancy Stanton, University of Notre Dame, South Bend, IN, USA"I have taught from an earlier edition of this very nice book. Both the students and I have been happy with it. It is an important and useful topic in math [both pure and applied], and it is especially relevant and central to the service courses offered by most math departments...Pinsky's book is the best text for teaching [the] classical tools...When students need to look up one of the classical formulas in the theory of boundary value problems, I often refer to Pinsky's book which has always been on target." - Palle E. T. Jorgensen, University of Iowa

Innehållsförteckning

PrefaceChapter 0. PreliminariesChapter 1. Fourier SeriesChapter 2. Boundary-Value Problems in Rectangular CoordinatesChapter 3. Boundary-Value Problems in Cylindrical CoordinatesChapter 4. Boundary-Value Problems in Spherical CoordinatesChapter 5. Fourier Transforms and ApplicationsChapter 6. Asymptotic AnalysisChapter 7. Numerical AnalysisChapter 8. Green's FunctionsAppendixesAnswers to Selected ExercisesIndexAbout the Author