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.
Higher Mathematics for Physics and Engineering Hiroyuki Shima · Tsuneyoshi Nakayama Higher Mathematics for Physics and Engineering 123 Dr. Hiroyuki Shima, Assistant Professor Department of Applied Physics Hokkaido University Sapporo 060-8628, Japan
[email protected] Dr. Tsuneyoshi Nakayama, Professor Toyota Physical and Chemical Research Institute Aichi 480-1192, Japan
[email protected] ISBN 978-3-540-87863-6 e-ISBN 978-3-540-87864-3 DOI 10.1007/b138494 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2009940406 c Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: eStudio Calamar Steinen Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) To our friends and colleagues Preface Owing to the rapid advances in the physical sciences and engineering, the demand for higher-level mathematics is increasing yearly. This book is designed for advanced undergraduates and graduate students who are interested in the mathematical aspects of their own fields of study. The reader is assumed to have a knowledge of undergraduate-level calculus and linear algebra. There are any number of books available on mathematics for physics and engineering but they all fall into one of two categories: the one emphasizes mathematical rigor and the exposition of definitions or theorems, wherea