Partial Differential Equations

by Gockenbach, Mark S.

• ISBN13: 9780898719352
• ISBN10: 0898719356
• Edition: 2nd
• Format: Hardcover
• Copyright: 2011-01-01
• Publisher: SOCIETY FOR INDUSTRIAL & APPLIED MATHEMATICS

Summary

Undergraduate courses on partial differential equations (PDEs) have traditionally been based on the Fourier series method for analysing and solving PDEs. What this textbook offers is a fresh approach; the traditional method taught alongside the modern finite element method. Both powerful methods are introduced to the reader and emphasised equally. A further beneficial feature of the book is that it uses the language of linear algebra, in particular in emphasising the role of best approximation in function spaces and the idea of an eigenfunction expansion. Its inclusion of realistic physical experiments for many examples and exercises will make the book appealing to science and engineering students, as well as students of mathematics. This second edition has a broader coverage of PDE methods and applications than the first, with the inclusion of chapters on the method of characteristics, Green's functions, SturmLiouville problems and a section on finite difference methods.

Table of Contents

Preface

Classification of differential equations

Models in one dimension

Essential linear algebra

Essential ordinary differential equations

Boundary value problems in statics

Heat flow and diffusion

Waves

First-order PDEs and the method of characteristics

Green's functions

Sturm-Liouville eigenvalue problems

Problems in multiple spatial dimensions

More about Fourier series

More about finite element methods

Proof of Theorem 3.47

Shifting the data in two dimensions

Bibliography

Index

Table of Contents provided by Publisher. All Rights Reserved.