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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.
V. Balakrishnan joined the Indian Institute of Technology Madras as a professor of physics in 1980, and retired as Professor Emeritus in 2013. He was educated at the University of Delhi and Brandeis University, USA, from where he got his PhD in theoretical particle physics in 1970. He joined IIT Madras after working for a decade at TIFR (Mumbai) and RRC, DAE (Kalpakkam). His research interests have spanned many areas over the years, including particle physics, many-body theory, condensed matter physics, stochastic processes, quantum dynamics, nonlinear dynamics and chaos. He has published numerous research papers in these areas and a number of popular pedagogic articles. He has co-authored a monograph titled Beyond the Crystalline State and authored a monograph titled Elements of Nonequilibrium Statistical Mechanics. Over nearly four decades, Dr. Balakrishnan has taught a wide variety of extremely popular courses at the undergraduate, masters and doctoral levels, comprising all the standard subjects in physics, as well as some new, non-traditional ones. He has received high accolades for his teaching at I IT Madras, and his lectures at numerous courses sponsored by the UGC, DST (SERC) and ICTP (Trieste, Italy) have been well-received by their attendees. His video lecture courses under the auspices of the NPTEL programme of the HRD Ministry (available on YouTube) have received very high acclaim. Dr. Balakrishnan has held visitin • •ositions at several institutions abroad. He is a Fellow of the Indian Academ of Sciences.
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.
