Multiple Integrals, Field Theory and Series

Description

The present book is based on lectures given by the authors at the Physical Department of the Lomonosov State University of Moscow. In the presentation of the material much emphasis has been placed on the physical meaning of mathematical notions and their interrela­tion as well as on the applications and computational aspects. Chapters 1-6 and Supplement 2 (On Universal Digital Computers) have been written by S.V. Fomin and Chapters 7-11 and Supple­ment 1 (Asymptotic Expansions) by B.M. Budak. The authors have discussed together the general plan of the book and many details concerning the presentation of the material. In the preparation of the book the authors have received valuable advice from their colleagues V.A. Ilyin, E.G. Poznyak, A.G. Sveshnikov and others. The authors owe very much to A.N. Tikhonov for his helpful comments and aid. Some important observations have been made by N.V. Yefimov and L.D. Kudryavtsev who have read the manuscript of the book. To all of them the authors express their warmest gratitude. CHAPTER 1. DOUBLE INTEGRALS CHAPTER 2. TRIPLE INTEGRALS AND MULTIPLE INTEGRALS OF HIGHER ORDER CHAPTER 3. ELEMENTS OF DIFFERENTIAL GEOMETRY CHAPTER 4. LINE INTEGRALS CHAPTER 5. SURFACE INTEGRALS CHAPTER 6. FIELD THEORY CHAPTER 7. TENSORS CHAPTER 8. FUNCTIONAL SEQUENCES AND SERIES CHAPTER 9. IMPROPER INTEGRALS CHAPTER 10. INTEGRALS DEPENDENT ON PARAMETER CHAPTER 11. FOURIER SERIES AND FOURIER INTEGRAL SUPPLEMENT 1. ASYMPTOTIC EXPANSIONS SUPPLEMENT 2. ON UNIVERSAL DIGITAL COMPUTERS Bibliography Name Index Subject Index