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Solution Techniques for Elementary Partial Differential Equations





ISBN 9781498704953
Published April 5, 2016 by Chapman and Hall/CRC
358 Pages - 56 B/W Illustrations

 
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Book Description

Solution Techniques for Elementary Partial Differential Equations, Third Edition remains a top choice for a standard, undergraduate-level course on partial differential equations (PDEs). Making the text even more user-friendly, this third edition covers important and widely used methods for solving PDEs.

New to the Third Edition

  • New sections on the series expansion of more general functions, other problems of general second-order linear equations, vibrating string with other types of boundary conditions, and equilibrium temperature in an infinite strip
  • Reorganized sections that make it easier for students and professors to navigate the contents
  • Rearranged exercises that are now at the end of each section/subsection instead of at the end of the chapter
  • New and improved exercises and worked examples
  • A brief Mathematica® program for nearly all of the worked examples, showing students how to verify results by computer

This bestselling, highly praised textbook uses a streamlined, direct approach to develop students’ competence in solving PDEs. It offers concise, easily understood explanations and worked examples that allow students to see the techniques in action.

Table of Contents

Ordinary Differential Equations: Brief Revision
First-Order Equations
Homogeneous Linear Equations with Constant Coefficients
Nonhomogeneous Linear Equations with Constant Coefficients
Cauchy–Euler Equations
Functions and Operators

Fourier Series
The Full Fourier Series
Fourier Sine and Cosine Series
Convergence and Differentiation
Series Expansion of More General Functions

Sturm–Liouville Problems
Regular Sturm–Liouville Problems
Other Problems
Bessel Functions
Legendre Polynomials
Spherical Harmonics

Some Fundamental Equations of Mathematical Physics
The Heat Equation
The Laplace Equation
The Wave Equation
Other Equations

The Method of Separation of Variables
The Heat Equation
The Wave Equation
The Laplace Equation
Other Equations
Equations with More Than Two Variables

Linear Nonhomogeneous Problems
Equilibrium Solutions
Nonhomogeneous Problems

The Method of Eigenfunction Expansion
The Nonhomogeneous Heat Equation
The Nonhomogeneous Wave Equation
The Nonhomogeneous Laplace Equation
Other Nonhomogeneous Equations

The Fourier Transformations
The Full Fourier Transformation
The Fourier Sine and Cosine Transformations
Other Applications

The Laplace Transformation
Definition and Properties
Applications

The Method of Green’s Functions
The Heat Equation
The Laplace Equation
The Wave Equation

General Second-Order Linear Equations
The Canonical Form
Hyperbolic Equations
Parabolic Equations
Elliptic Equations
Other Problems

The Method of Characteristics
First-Order Linear Equations
First-Order Quasilinear Equations
The One-Dimensional Wave Equation
Other Hyperbolic Equations

Perturbation and Asymptotic Methods
Asymptotic Series
Regular Perturbation Problems
Singular Perturbation Problems

Complex Variable Methods
Elliptic Equations
Systems of Equations

Appendix

Further Reading

Index

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Author(s)

Biography

Christian Constanda, MS, PhD, DSc, is the Charles W. Oliphant Endowed Chair in Mathematical Sciences and director of the Center for Boundary Integral Methods at the University of Tulsa. He is also an emeritus professor at the University of Strathclyde and chairman of the International Consortium on Integral Methods in Science and Engineering. He is the author/editor of more than 28 books and more than 130 journal papers. His research interests include boundary value problems for elastic plates with transverse shear deformation, direct and indirect integral equation methods for elliptic problems and time-dependent problems, and variational methods in elasticity.

Reviews

"The author, a skilled classroom performer with considerable experience, understands exactly what students want and has given them just that: a textbook that explains the essence of the method briefly and then proceeds to show it in action. … A new and very helpful element added to the third edition is the insertion of Mathematica® software code at the end of each worked example, which shows how the computed solution to a problem can be verified by computer. The distribution of the exercises to each relevant section and subsection instead of having them bunched up together at the end of the chapter is also a welcome development. In my opinion, this is quite simply the best book of its kind that I have seen thus far. The book not only contains solution methods for some very important classes of PDEs, in an easy-to-read format, but is also student-friendly and teacher-friendly at the same time. It is definitely a textbook for adoption."
—From the Foreword by Professor Peter Schiavone, Department of Mechanical Engineering, University of Alberta, Edmonton, Canada

Praise for the Second Edition:
"… an interesting read. … Some of the worked-out examples cover not only the conventional topics of heat and wave problems but also applications to a wide variety of fields, from stock markets to Brownian motion. … Each chapter has many problems for practice, with solutions for some of them provided at the very end. The book is well written, concise, has adequate examples and can be used as a textbook for beginners to learn the techniques of PDE solvers."
MAA Reviews, January 2011

"This concise, well-written book, which includes a profusion of worked examples and exercises, serves both as an excellent text in undergraduate and graduate learning and as a useful presentation of solution techniques for researchers and engineers interested in applying partial differential equations to real-life problems."
—Barbara Zubik-Kowal, Boise State University, Idaho, USA

Praise for the First Edition:
"The book contains a large number of worked examples and exercises. … Useful for the … student who might be interested … in learning the manipulating skills of solution methods of first- and second-order partial differential equations."
Zentralblatt MATH, 1042

Winner of a 2002 CHOICE Outstanding Academic Title Award
"… an easy-to-read and straight-to-the-point book for all those who want to familiarize themselves with concepts and solution techniques for partial differential equations … A writing style special to this author is the complete departure from the arid theorem-proof approach to PDEs. Abstract concepts are carefully explained and supported with a wealth of remarks, application-oriented illustrations, and a wonderful collection of problems, a few elementary enough for any beginner. On the whole, the material is very well presented; this is one of the best books on elementary PDEs this reviewer has read so far. Highly recommended."
CHOICE, October 2002

"… successfully addresses a difficult problem of undergraduate teaching: how to make students understand and become adept at using a class of practical tools that are essential in the study of many mathematical models … clear, concise, and easy to read—places the emphasis on worked examples and exercises … . Someone who needs a book that goes straight to the point and shows what partial differential equations are and how they can be solved, should find this textbook to be one of the best suited for the purpose."
—Barbara Bertram, Michigan Technological University, Houghton, USA

"… an invaluable resource. … The fact that no computing devices are needed to work through this text is a distinct advantage … an ideal tool for students taking a first course in PDEs, as well as for the lecturers who teach such courses."
—Marian Aron, Plymouth University, UK

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