Hardcover ISBN:  9780821868898 
Product Code:  AMSTEXT/15 
List Price:  $88.00 
MAA Member Price:  $79.20 
AMS Member Price:  $70.40 
Electronic ISBN:  9781470411282 
Product Code:  AMSTEXT/15.E 
List Price:  $83.00 
MAA Member Price:  $74.70 
AMS Member Price:  $66.40 

Book DetailsPure and Applied Undergraduate TextsVolume: 15; 1998; 526 ppMSC: Primary 35;
Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundaryvalue 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 threedimensional 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 steadystate 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.ReadershipUndergraduate students interested in PDE and applied PDE.

Table of Contents

Cover

Title page

Copyright

Preface

Contents

Chapter 0. Preliminaries

Chapter 1. Fourier series

Chapter 2. Boundaryvalue problems in rectangular coordinates

Chapter 3. Boundaryvalue problems in cylindrical coordinates

Chapter 4. Boundaryvalue problems in spherical coordinates

Chapter 5. Fourier transforms and applications

Chapter 6. Asymptotic analysis

Chapter 7. Numerical analysis

Chapter 8. Green’s functions

Appendixes

Answers to selected exercises

Index

About the Author

Back Cover


Additional Material

Reviews

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 WisconsinMadison, Madison, WI 
I have used Partial Differential Equations and BoundaryValue 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


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Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundaryvalue 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 threedimensional 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 steadystate 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.
Undergraduate students interested in PDE and applied PDE.

Cover

Title page

Copyright

Preface

Contents

Chapter 0. Preliminaries

Chapter 1. Fourier series

Chapter 2. Boundaryvalue problems in rectangular coordinates

Chapter 3. Boundaryvalue problems in cylindrical coordinates

Chapter 4. Boundaryvalue problems in spherical coordinates

Chapter 5. Fourier transforms and applications

Chapter 6. Asymptotic analysis

Chapter 7. Numerical analysis

Chapter 8. Green’s functions

Appendixes

Answers to selected exercises

Index

About the Author

Back Cover

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 WisconsinMadison, Madison, WI 
I have used Partial Differential Equations and BoundaryValue 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