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Higher Mathematics for Physics and Engineering written by
Hiroyuki Shima , Assistant Professor, Department of Applied Physics, Hokkaido University, Sapporo 060-8628, Japan, shima@eng.hokudai.ac.jp and
Tsuneyoshi Nakayama , Professor, Aichi 480-1192, Japan, Riken-nakayama@mosk.tytlabs.co.jp.
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.
Title: Higher Mathematics for Physics and Engineering
Edition:
Author(s): Hiroyuki Shima, Tsuneyoshi Nakayama
Publisher: Springer-Verlag Berlin Heidelberg
Series:
Year: 2010
Pages: 711
Type: PDF
Language: English
ISBN: 9783540878636,3540878637
Country: Japan
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Higher Mathematics for Physics and Engineering written by
Hiroyuki Shima, Tsuneyoshi Nakayama
cover the following topics.
1. Preliminaries
Part-I Real Analysis
2. Real Sequences and Series
3. Real Functions
Part-II Functional Analysis
4. Hilbert Spaces
5. Orthonormal Polynomials
6. Lebesgue Integrals
Part-III Complex Analysis
7. Complex Functions
8. Singularity and Continuation
9. Contour Integrals
10. Conformal Mapping
Part-IV Fourier Analysis
11. Fourier Series
12. Fourier Transformation
13. Laplace Transformation
14. Wavelet Transformation
Part-V Differential Equations
15. Ordinary Differential Equations
16. System of Ordinary Differential Equations
17. Partial Differential Equations
Part-VI Tensor Analyses
18. Cartesian Tensors
19. Non-Cartesian Tensors
20. Tensor as Mapping
Part-VII Appendixes
A Proof of the Bolzano–Weierstrass Theorem
A.1 Limit Points
A.2 Cantor Theorem
A.3 Bolzano–Weierstrass Theorem
B Diracd Function
B.1 Basic Properties
B.2 Representation as a Limit of Function
B.3 Remarks on Representation 4
C Proof of Weierstrass Approximation Theorem
D Tabulated List of Orthonormal Polynomial Functions
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