Mathematical Physics with Applications, Problems and Solutions by V. Balakrishnan

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Mathematical Physics with Applications, Problems and Solutions

by V. Balakrishnan

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This book gives a comprehensive account of mathematical physics, assigning a prominent role to the applications of the relevant mathematics to specific parts of physics ranging overfluid mechanics, electromagnetic theory, special relativity, quantum mechanics, quantum optics, random processes, linear response theory, scattering theory, and so on. Rather than emphasising formal proofs of propositions, the results are motivated, stated, elaborated and remarked upon. Their inter-relationships and connections are brought out, and several of their applications are discussed in some detail. There are about 370 exercises and problems interspersed in the text itself at appropriate junctures, so as to facilitate the logical flow of the material without interruption. Wherever applicable, solutions to the problems, or answers with hints as to how to arrive at them, along with relevant remarks, are given at the end of each chapter. This book can also be used as a wide-ranging and fairly self-contained text for self-study, and will be well received by students of physics at all levels (senior undergraduate, masters and doctoral), as well as those who are now teachers of the subject. Contents: 1. Warming up: Functions of a real variable 2. Gaussian integrals, Stirlings formula, & some integrals 3. Some more functions 4. Generalized functions 5. Vectors and tensors 6. Vector calculus 7. A bit of fluid dynamics 8. Some more vector calculus 9. A bit of electromagnetism and special relativity 10. Linear vector spaces 11. A look at matrices 12. More about matrices 13. Infinite-dimensional vector spaces 14. Linear operators on a vector space 15. Operator algebras and identities 16. Orthogonal polynomials 17. Fourier series 18. Fourier integrals 19. Discrete probability distributions 20. Continuous probability distributions 21. Stochastic processes 22. Analytic functions of a complex variable 23. More on analytic functions 24. Linear response and analyticity 25. Analytic continuation and the gamma function 26. Multivalued functions and integral representations 27. Mobius transformations 28. Laplace transforms 29. Green function for the Laplacian operator 30. The diffusion equation 31. The wave equation 32. Integral equations, Bibliography & Further Reading, Index. ISBN - 9789386761118

Pages : 878

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