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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.
List of contents
Preliminaries.- I Real Analysis.- Real Sequences and Series.- Real Functions.- II Functional Analysis.- Hilbert Spaces.- Orthonormal Polynomials.- Lebesgue Integrals.- III Complex Analysis.- Complex Functions.- Singularity and Continuation.- Contour Integrals.- Conformal Mapping.- IV Fourier Analysis.- Fourier Series.- Fourier Transformation.- Laplace Transformation.- Wavelet Transformation.- V Differential Equations.- Ordinary Differential Equations.- System of Ordinary Differential Equations.- Partial Differential Equations.- VI Tensor Analyses.- Cartesian Tensors.- Non-Cartesian Tensors.- Tensor as Mapping.
About the author
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 Montpellier, 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.
Summary
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.
Additional text
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)
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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)
