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Higher Mathematics for Physics and Engineering

Mathematical Methods for Contemporary Physics

  • Tsuneyoshi Nakayama
  • Hiroyuki Shima

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Hiroyuki Shima, Tsuneyoshi Nakayama
    Pages 1-13
  3. Real Analysis

    1. Front Matter
      Pages 15-15
    2. Hiroyuki Shima, Tsuneyoshi Nakayama
      Pages 17-44
    3. Hiroyuki Shima, Tsuneyoshi Nakayama
      Pages 45-70
  4. Functional Analysis

    1. Front Matter
      Pages 71-71
    2. Hiroyuki Shima, Tsuneyoshi Nakayama
      Pages 73-99
    3. Hiroyuki Shima, Tsuneyoshi Nakayama
      Pages 101-137
    4. Hiroyuki Shima, Tsuneyoshi Nakayama
      Pages 139-181
  5. Complex Analysis

    1. Front Matter
      Pages 183-183
    2. Hiroyuki Shima, Tsuneyoshi Nakayama
      Pages 185-232
    3. Hiroyuki Shima, Tsuneyoshi Nakayama
      Pages 233-257
    4. Hiroyuki Shima, Tsuneyoshi Nakayama
      Pages 259-303
    5. Hiroyuki Shima, Tsuneyoshi Nakayama
      Pages 305-336
  6. Fourier Analysis

    1. Front Matter
      Pages 337-337
    2. Hiroyuki Shima, Tsuneyoshi Nakayama
      Pages 339-375
    3. Hiroyuki Shima, Tsuneyoshi Nakayama
      Pages 377-406
    4. Hiroyuki Shima, Tsuneyoshi Nakayama
      Pages 407-448
    5. Hiroyuki Shima, Tsuneyoshi Nakayama
      Pages 449-480
  7. Differential Equations

    1. Front Matter
      Pages 481-481
    2. Hiroyuki Shima, Tsuneyoshi Nakayama
      Pages 483-507
    3. Hiroyuki Shima, Tsuneyoshi Nakayama
      Pages 509-538
    4. Hiroyuki Shima, Tsuneyoshi Nakayama
      Pages 539-562
  8. Tensor Analyses

    1. Front Matter
      Pages 563-563
    2. Hiroyuki Shima, Tsuneyoshi Nakayama
      Pages 565-600
    3. Hiroyuki Shima, Tsuneyoshi Nakayama
      Pages 601-637
    4. Hiroyuki Shima, Tsuneyoshi Nakayama
      Pages 639-653
  9. Back Matter
    Pages 655-688

About this book

Introduction

Due to the rapid expansion of the frontiers of physics and engineering, the demand for higher-level mathematics is increasing yearly. This book is designed to provide accessible knowledge of higher-level mathematics demanded in contemporary physics and engineering. Rigorous mathematical structures of important subjects in these fields are fully covered, which will be helpful for readers to become acquainted with certain abstract mathematical concepts. The selected topics are:

- Real analysis, Complex analysis, Functional analysis, Lebesgue integration theory, Fourier analysis, Laplace analysis, Wavelet analysis, Differential equations, and Tensor analysis.

This book is essentially self-contained, and assumes only standard undergraduate preparation such as elementary calculus and linear algebra. It is thus well suited for graduate students in physics and engineering who are interested in theoretical backgrounds of their own fields. Further, it will also be useful for mathematics students who want to understand how certain abstract concepts in mathematics are applied in a practical situation. The readers will not only acquire basic knowledge toward higher-level mathematics, but also imbibe mathematical skills necessary for contemporary studies of their own fields.

Keywords

Analysis Applied mathematics Mathematical physics textbook Mathematical topology for knot theory Mathematics for physics and engineers Textbook on mathematical methods Transformation Wavelet linear algebra linear optimization

Authors and affiliations

  • Tsuneyoshi Nakayama
    • 1
  • Hiroyuki Shima
    • 2
  1. 1.Research InstituteToyota Physical & ChemicalAichiJapan
  2. 2.Dept. Applied PhysicsHokkaido UniversitySapporoJapan

Bibliographic information

  • DOI https://doi.org/10.1007/b138494
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-540-87863-6
  • Online ISBN 978-3-540-87864-3
  • Buy this book on publisher's site
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