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Applied Partial Differential Equations

  • J. David Logan

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. J. David Logan
    Pages 91-115
  3. Back Matter
    Pages 169-184

About this book

Introduction

This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems;' The audience usually consists of stu­ dents in mathematics, engineering, and the physical sciences. The topics include derivations of some of the standard equations of mathemati­ cal physics (including the heat equation, the· wave equation, and the Laplace's equation) and methods for solving those equations on bounded and unbounded domains. Methods include eigenfunction expansions or separation of variables, and methods based on Fourier and Laplace transforms. Prerequisites include calculus and a post-calculus differential equations course. There are several excellent texts for this course, so one can legitimately ask why one would wish to write another. A survey of the content of the existing titles shows that their scope is broad and the analysis detailed; and they often exceed five hundred pages in length. These books gen­ erally have enough material for two, three, or even four semesters. Yet, many undergraduate courses are one-semester courses. The author has often felt that students become a little uncomfortable when an instructor jumps around in a long volume searching for the right topics, or only par­ tially covers some topics; but they are secure in completely mastering a short, well-defined introduction. This text was written to proVide a brief, one-semester introduction to partial differential equations.

Keywords

Boundary value problem Fourier series Laplace's equation calculus differential equation ordinary differential equation partial differential equation wave equation

Authors and affiliations

  • J. David Logan
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of Nebraska at LincolnLincolnUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-0533-0
  • Copyright Information Springer-Verlag New York 1998
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-98439-1
  • Online ISBN 978-1-4684-0533-0
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site