Overview
Includes the latest developments in physics- and engineering-oriented higher mathematics, such as for quantum information theory and mathematical topology for knot theory.- Exposition of mathematical concepts underlying physical phenomena.- Combines mathematical rigour with practical applications.- Offers learning and teaching aids as worked-out examples with solutions for the application of higher mathematics in physics and engineering.- Reader-friendly summaries in each chapter
Includes supplementary material: sn.pub/extras
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Table of contents (20 chapters)
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Front Matter
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Real Analysis
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Front Matter
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Part I Real Analysis
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Functional Analysis
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Front Matter
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Part II Functional Analysis
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Complex Analysis
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Front Matter
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Part III Complex Analysis
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Fourier Analysis
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Front Matter
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Part IV Fourier Analysis
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Differential Equations
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Front Matter
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Keywords
About this book
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.
Reviews
From the reviews:
“This is a largely self-contained exposition of fundamental topics in the mathematics of physics and engineering, which … will lead to an understanding of the symbiotic relationship between mathematics and the physical sciences. … The exercises … are solved in full immediately after the problem statements. … It may be most useful for graduate students and as a reference for professionals. Summing Up: Recommended. Upper-division undergraduate through professional collections.” (D. Robbins, Choice, Vol. 48 (5), January, 2011)
“This delightful text has been written for advanced undergraduates and graduate students in engineering and physics who need substantial mathematical knowledge for further studies in their own fields. It provides a well-balanced blend of theory and applications. The exposition is very well planned, detailed and emphasizes rigor and clarity. … This is a truly exceptional book. … Highly recommended guide to advanced mathematics behind important topics in engineering and physics.” (Yuri V. Rogovchenko, Zentralblatt MATH, Vol. 1200, 2011)
Authors and Affiliations
About the authors
Tsuneyoshi Nakayama
graduated from Hokkaido University in Japan in 1973. He is a professor of Theoretical Condensed Matter Physics in Department of Applied Physics in Hokkaido University from 1986. During this period he stayed Max-Planck Institute, University of Monpellier, University of Cambridge, and The University of Tokyo. He is the co-author of the book "Fractal concepts of condensed matter."Hiroyuki Shima
obtained Ph.D from Hokkaido University. He is currently pursuing his studies, with a special interest in critical phenomena in disordered systems and many-body problems in complex systems. He has had a considerable amount of experience in teaching mathematics and physics to undergraduate and graduate students.Bibliographic Information
Book Title: Higher Mathematics for Physics and Engineering
Authors: Tsuneyoshi Nakayama, Hiroyuki Shima
DOI: https://doi.org/10.1007/b138494
Publisher: Springer Berlin, Heidelberg
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2010
Hardcover ISBN: 978-3-540-87863-6Published: 27 April 2010
Softcover ISBN: 978-3-642-42591-2Published: 11 November 2014
eBook ISBN: 978-3-540-87864-3Published: 12 April 2010
Edition Number: 1
Number of Pages: XXI, 688
Topics: Theoretical, Mathematical and Computational Physics, Mathematical and Computational Engineering, Applications of Mathematics, Mathematical Methods in Physics, Analysis