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. Instead it emphasizes the mathematical concepts underlying manifold physical phenomena. The readers will not only acquire knowledge required in actual applications, but also acquire the minimum ‘mathematical skills’ necessary in the study of physics. Making the text coherentand self-contained, it states and 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, and sentences beginning with ‘it may be shown that ’ are kept to the minimum. Each chapter containsa number of examples and practice exercises. Such a large number of examples provide the balance between mathematical formalisms and their applications. Very useful and up-to-date textbook on mathematical physics, physical mathematics and mathematical methods in engineering INDICE: 1. Preliminaries.- 2. 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.
- ISBN: 978-3-540-87863-6
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 720
- Fecha Publicación: 01/11/2008
- Nº Volúmenes: 1
- Idioma: Inglés