Higher Mathematics for Physics and Engineering Mathematical Methods for Contemporary Physics /

• Main Authors: Nakayama, Tsuneyoshi. (Author), Shima, Hiroyuki. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Subjects: Physics.; Global analysis (Mathematics).; Mathematics.; Mathematical physics.; Engineering mathematics.; Theoretical, Mathematical and Computational Physics.; Appl.Mathematics/Computational Methods of Engineering.; Applications of Mathematics.; Mathematical Methods in Physics.; Analysis.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/b138494

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 o...

Table of Contents:

• 1. Preliminaries
• 2. Real Sequences and Series
• 3. Real Functions
• 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.