Higher Mathematics for Physics and Engineering
Mathematical Methods for Contemporary Physics
(Sprache: Englisch)
Differing from many mathematics texts, this one emphasizes the mathematical concepts underlying manifold physical phenomena. Readers get both the knowledge required in applications, and also the minimum "mathematical skills" necessary in the study of physics.
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Produktinformationen zu „Higher Mathematics for Physics and Engineering “
Differing from many mathematics texts, this one emphasizes the mathematical concepts underlying manifold physical phenomena. Readers get both the knowledge required in applications, and also the minimum "mathematical skills" necessary in the study of physics.
Klappentext zu „Higher Mathematics for Physics and Engineering “
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 usefulfor 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.
Mathematics for physics and engineering are traditionally covered in textbooks such as "Mathematical Physics" or "Applied Mathematics". This book differs from those on pure mathematics and differs from lexicographic collections of methods for solving specific problems. Insetad it emphasizes the mathematical concepts underlying manifold physical phenomena.
The readers will not only acquire knowledges required in actual applications, but also acquire the minimum "mathematical skills" necessary to study physics.
Making the text coherent and self-contained, it states nd proves a large number of theorems, lemmas, and corollaries that are relevant to physics and other related sciences. Extensive details on mathematical manipulations are provided.
Each chapter contains a number of examples and practical exercises. Such a large number of examples provides the balance between mathematical formalisms and their applications. Reflecting current interests, several new topics concerning developing fields, such as the mathematical background of quantum information theory and topology for the knot theory, are included.
The readers will not only acquire knowledges required in actual applications, but also acquire the minimum "mathematical skills" necessary to study physics.
Making the text coherent and self-contained, it states nd proves a large number of theorems, lemmas, and corollaries that are relevant to physics and other related sciences. Extensive details on mathematical manipulations are provided.
Each chapter contains a number of examples and practical exercises. Such a large number of examples provides the balance between mathematical formalisms and their applications. Reflecting current interests, several new topics concerning developing fields, such as the mathematical background of quantum information theory and topology for the knot theory, are included.
Inhaltsverzeichnis zu „Higher Mathematics for Physics and Engineering “
1. Preliminaries2. Real Sequences and Series
3. Real Function
4. Hilbert Spaces
5. Orthonormal Polynomials
6. Lebesgue Integrals
7. Complex Functions
8. Singularity and Continuation
9. Contour Integrals
10. Conformal Mapping
11. Fourier Series
12. Fourier Transformation
13. Laplace Transformation
14. Wavelet Transformation
15. Ordinary Differential Equations
16. System of Ordinary Differential Equations
17. Partial Differential Equations
18. Cartesian Tensors
19. Non-Cartesian Tensors
20. Tensor as Mapping
A. Proof of the Bolzano-Weierstrass Theorem
B. Dirac's delta-Function
C. Proof of Weierstrass' Approximation Theorem
D. Tabulated List of Orthonormal Polynomial Functions
Autoren-Porträt von Hiroyuki Shima, Tsuneyoshi Nakayama
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.
Bibliographische Angaben
- Autoren: Hiroyuki Shima , Tsuneyoshi Nakayama
- 2010, 2010, 688 Seiten, mit Abbildungen, Masse: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 3540878637
- ISBN-13: 9783540878636
- Erscheinungsdatum: 27.04.2010
Sprache:
Englisch
Rezension zu „Higher Mathematics for Physics and Engineering “
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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