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Potential Theory

  • John Wermer

Table of contents

  1. Front Matter
    Pages N2-VIII
  2. John Wermer
    Pages 1-10
  3. John Wermer
    Pages 11-16
  4. John Wermer
    Pages 17-25
  5. John Wermer
    Pages 26-33
  6. John Wermer
    Pages 34-40
  7. John Wermer
    Pages 50-55
  8. John Wermer
    Pages 60-65
  9. John Wermer
    Pages 74-83
  10. John Wermer
    Pages 84-90
  11. John Wermer
    Pages 91-99
  12. John Wermer
    Pages 100-107
  13. John Wermer
    Pages 108-113
  14. John Wermer
    Pages 114-128
  15. John Wermer
    Pages 129-137
  16. John Wermer
    Pages 138-140
  17. John Wermer
    Pages 141-143
  18. John Wermer
    Pages 144-145
  19. Back Matter
    Pages 146-149

About this book

Introduction

Potential theory grew out of mathematical physics, in particular out of the theory of gravitation and the theory of electrostatics. Mathematical physicists such as Poisson and Green introduced some of the central ideas of the subject. A mathematician with a general knowledge of analysis may find it useful to begin his study of classical potential theory by looking at its physical origins. Sections 2, 5 and 6 of these Notes give in part heuristic arguments based on physical considerations. These heuristic arguments suggest mathematical theorems and provide the mathematician with the problem of finding the proper hypotheses and mathematical proofs. These Notes are based on a one-semester course given by the author at Brown University in 1971. On the part of the reader, they assume a knowledge of Real Function Theory to the extent of a first year graduate course. In addition some elementary facts regarding harmonic functions are aS$umed as known. For convenience we have listed these facts in the Appendix. Some notation is also explained there. Essentially all the proofs we give in the Notes are for Euclidean 3-space R3 and Newtonian potentials ~.

Keywords

Mathematica Potential theory function mathematical physics mathematical proof proof theorem

Authors and affiliations

  • John Wermer
    • 1
  1. 1.Brown UniversityProvidenceUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-12727-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 1974
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-06857-0
  • Online ISBN 978-3-662-12727-8
  • Buy this book on publisher's site