Cover for Advanced Calculus and Vector Field Theory

Advanced Calculus and Vector Field Theory

Book1966

Authors:

KATHLEEN M. URWIN

Advanced Calculus and Vector Field Theory

Book1966

 

Cover for Advanced Calculus and Vector Field Theory

Authors:

KATHLEEN M. URWIN

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Book description

THIS book falls naturally into two parts. In Chapters 1-5 the basic ideas and techniques of partial differentiation, and of line, multiple and surface integrals are discussed. Chap ... read full description

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  2. Book chapterAbstract only

    CHAPTER 1 - INTRODUCTION

    Pages 1-7

  3. Book chapterAbstract only

    CHAPTER 2 - FUNCTIONS OF SEVERAL INDEPENDENT VARIABLES

    Pages 8-33

  4. Book chapterAbstract only

    CHAPTER 3 - LINE INTEGRALS

    Pages 34-49

  5. Book chapterAbstract only

    CHAPTER 4 - MULTIPLE INTEGRALS

    Pages 50-91

  6. Book chapterAbstract only

    CHAPTER 5 - SURFACE INTEGRALS

    Pages 92-110

  7. Book chapterAbstract only

    CHAPTER 6 - VECTOR FIELD THEORY (1)

    Pages 111-146

  8. Book chapterAbstract only

    CHAPTER 7 - VECTOR FIELD THEORY (2)

    Pages 147-196

  9. Book chapterAbstract only

    CHAPTER 8 - APPLICATIONS OF VECTOR FIELD THEORY

    Pages 197-254

  10. Book chapterNo access

    ANSWERS TO EXERCISES

    Pages 255-261

  11. Book chapterNo access

    Index

    Pages 263-265

  12. Book chapterNo access

    Inside Back Matter

    Page ibc1

About the book

Description

THIS book falls naturally into two parts. In Chapters 1-5 the basic ideas and techniques of partial differentiation, and of line, multiple and surface integrals are discussed. Chapters 6 and 7 give the elements of vector field theory, taking the integral definitions of the divergence and curl of a vector field as their starting points; the last chapter surveys very briefly some of the immediate applications of vector field theory to five branches of applied mathematics. Throughout I have given numerous worked examples. In these I have paid particular attention to those points which in my own experience I have found to give most difficulty to students. In the text I have denoted spherical polar coordinates by (/-, 0, ψ)9 and cylindrical polar coordinates by (p, ψ, ζ), so that ψ measures the same angle in both systems. Since there is no one standard notation for these systems, the reader will meet different notations in the course of his reading, and in quoting examination questions in the exercises I have kept to the notation of the originals. The Exercises at the end of each section are intended to give practice in the basic techniques just discussed. The Miscellaneous Exercises are more varied, and contain many examination questions.

THIS book falls naturally into two parts. In Chapters 1-5 the basic ideas and techniques of partial differentiation, and of line, multiple and surface integrals are discussed. Chapters 6 and 7 give the elements of vector field theory, taking the integral definitions of the divergence and curl of a vector field as their starting points; the last chapter surveys very briefly some of the immediate applications of vector field theory to five branches of applied mathematics. Throughout I have given numerous worked examples. In these I have paid particular attention to those points which in my own experience I have found to give most difficulty to students. In the text I have denoted spherical polar coordinates by (/-, 0, ψ)9 and cylindrical polar coordinates by (p, ψ, ζ), so that ψ measures the same angle in both systems. Since there is no one standard notation for these systems, the reader will meet different notations in the course of his reading, and in quoting examination questions in the exercises I have kept to the notation of the originals. The Exercises at the end of each section are intended to give practice in the basic techniques just discussed. The Miscellaneous Exercises are more varied, and contain many examination questions.

Details

ISBN

978-1-4831-6785-5

Language

English

Published

1966

Copyright

Copyright © 1966 Elsevier Ltd. All rights reserved.

Imprint

Pergamon

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Authors

KATHLEEN M. URWIN

Department of Mathematics, Battersea College of Technology