Synopsis
This textbook is aimed at advanced undergraduate and graduate students interested in learning the fundamental mathematical concepts and tools widely used in different areas of physics. The author draws on a vast teaching experience, and presents a comprehensive and self-contained text which explains how mathematics intertwines with and forms an integral part of physics in numerous instances. Rather than emphasizing rigorous proofs of theorems, specific examples and physical applications (such as fluid dynamics, electromagnetism, quantum mechanics, etc.) are invoked to illustrate and elaborate upon the relevant mathematical techniques. The early chapters of the book introduce different types of functions, vectors and tensors, vector calculus, and matrices. In the subsequent chapters, more advanced topics like linear spaces, operator algebras, special functions, probability distributions, stochastic processes, analytic functions, Fourier series and integrals, Laplace transforms, Green's functions and integral equations are discussed. The book also features about 400 exercises and solved problems interspersed throughout the text at appropriate junctures, to facilitate the logical flow and to test the key concepts. Overall this book will be a valuable resource for a wide spectrum of students and instructors of mathematical physics. This textbook is aimed at advanced undergraduate and graduate students interested in learning the fundamental mathematical concepts and tools widely used in different areas of physics. The author draws on a vast teaching experience, and presents a comprehensive and self-contained text which explains how mathematics intertwines with and forms an integral part of physics in numerous instances. Rather than emphasizing rigorous proofs of theorems, specific examples and physical applications (such as fluid dynamics, electromagnetism, quantum mechanics, etc.) are invoked to illustrate and elaborate upon the relevant mathematical techniques. The
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Mathematical Physics : with Applications, Problems and Solutions
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Soft cover. Condition: New. ISBN:9789388264822. Seller Inventory # 2483266
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Mathematical Physics with Applications, Problems and Solutions
Seller: Vedams eBooks (P) Ltd, New Delhi, India
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Soft cover. Condition: New. Contents: 1. Warming up: Functions of a real variable. 2. Gaussian integrals, Stirlings formula and 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. Multi-valued 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 and Further Reading. Index. 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. Seller Inventory # 131128