**Pure and Applied Undergraduate Texts**

Volume: 15;
1998;
526 pp;
Hardcover

MSC: Primary 35;

**Print ISBN: 978-0-8218-6889-8
Product Code: AMSTEXT/15**

List Price: $88.00

AMS Member Price: $70.40

MAA Member Price: $79.20

**Electronic ISBN: 978-1-4704-1128-2
Product Code: AMSTEXT/15.E**

List Price: $83.00

AMS Member Price: $66.40

MAA Member Price: $74.70

#### Supplemental Materials

# Partial Differential Equations and Boundary-Value Problems with Applications: Third Edition

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*Mark A. Pinsky*

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.

#### Readership

Undergraduate students interested in PDE and applied PDE.

#### Reviews & Endorsements

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

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

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

#### Table of Contents

# Table of Contents

## Partial Differential Equations and Boundary-Value Problems with Applications: Third Edition

- Cover Cover11 free
- Title page iii4 free
- Copyright iv5 free
- Preface v6 free
- Contents ix10 free
- Chapter 0. Preliminaries 116 free
- Chapter 1. Fourier series 3550
- Chapter 2. Boundary-value problems in rectangular coordinates 99114
- Chapter 3. Boundary-value problems in cylindrical coordinates 171186
- Chapter 4. Boundary-value problems in spherical coordinates 235250
- Chapter 5. Fourier transforms and applications 277292
- Chapter 6. Asymptotic analysis 345360
- Chapter 7. Numerical analysis 379394
- Chapter 8. Green’s functions 427442
- Appendixes 465480
- Answers to selected exercises 503518
- Index 521536
- About the Author 527542
- Back Cover Back Cover1545