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Multiple Integrals

  • Authors
  • Walter Ledermann

Part of the Library of Mathematics book series (LIMA)

Table of contents

  1. Front Matter
    Pages N2-vi
  2. Walter Ledermann
    Pages 1-21
  3. Walter Ledermann
    Pages 22-67
  4. Walter Ledermann
    Pages 68-79
  5. Walter Ledermann
    Pages 80-98
  6. Back Matter
    Pages 99-107

About this book

Introduction

The aim of this book is to give an elementary treatment of multiple integrals. The notions of integrals extended over a curve, a plane region, a surface and a solid are introduced in tum, and methods for evaluating these integrals are presented in detail. Especial reference is made to the results required in Physics and other mathematical sciences, in which multiple integrals are an indispensable tool. A full theoretical discussion of this topic would involve deep problems of analysis and topology, which are outside the scope of this volume, and concessions had to be made in respect of completeness without, it is hoped, impairing precision and a reasonable standard of rigour. As in the author's Integral Calculus (in this series), the main existence theorems are first explained informally and then stated exactly, but not proved. Topological difficulties are circumvented by imposing some­ what stringent, though no unrealistic, restrictions on the regions of integration. Numerous examples are worked out in the text, and each chapter is followed by a set of exercises. My thanks are due to my colleague Dr. S. Swierczkowski, who read the manuscript and made valuable suggestions. w. LEDERMANN The University of Sussex, Brighton.

Keywords

Area Gauss’s Theorem Green’s Theorem Stokes’s Theorem boundary element method curvilinear integral double integral exercise formation line integral multiple integral surface integral surfaces theorem volume integral

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-011-6091-9
  • Copyright Information Springer Science+Business Media B.V. 1966
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-7100-4358-0
  • Online ISBN 978-94-011-6091-9
  • Buy this book on publisher's site