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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

** Download from Amazon : **

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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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- Differential Equacitons
- Fourier Analysis
- Linear Algebra
- Matrix Calculus
- Vector Analysis
- Tensor Calculus
- Probability & Statistics
- Discrete Mathematics

- Abstract Algebra
- Calculus
- Differential Equations
- Engineering Mathematics
- Linear Algebra
- Math Magic
- Real Analysis