Mathematical Physics

1. Front Matter

   Pages i-xxvii

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2. Warming Up: Functions of a Real Variable

   • V. Balakrishnan

   Pages 1-7

3. Gaussian Integrals, Stirling’s Formula, and Some Integrals

   • V. Balakrishnan

   Pages 9-17

4. Some More Functions

   • V. Balakrishnan

   Pages 19-28

5. Generalized Functions

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   Pages 29-41

6. Vectors and Tensors

   • V. Balakrishnan

   Pages 43-71

7. Vector Calculus

   • V. Balakrishnan

   Pages 73-96

8. A Bit of Fluid Dynamics

   • V. Balakrishnan

   Pages 97-111

9. Some More Vector Calculus

   • V. Balakrishnan

   Pages 113-136

10. A Bit of Electromagnetism and Special Relativity

    • V. Balakrishnan

    Pages 137-162

11. Linear Vector Spaces

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    Pages 163-176

12. A Look at Matrices

    • V. Balakrishnan

    Pages 177-199

13. More About Matrices

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    Pages 201-238

14. Infinite-Dimensional Vector Spaces

    • V. Balakrishnan

    Pages 239-251

15. Linear Operators on a Vector Space

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    Pages 253-280

16. Operator Algebras and Identities

    • V. Balakrishnan

    Pages 281-318

17. Orthogonal Polynomials

    • V. Balakrishnan

    Pages 319-359

18. Fourier Series

    • V. Balakrishnan

    Pages 361-374

19. Fourier Integrals

    • V. Balakrishnan

    Pages 375-392

20. Discrete Probability Distributions

    • V. Balakrishnan

    Pages 393-419

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. 

 

• Vector calculus and applications
• Linear vector spaces, matrices and operators
• Probability, statistics and random processes
• Complex analysis
• Special functions
• Partial differential equations
• Electrostatics
• Magnetostatics
• Infinite dimensional vector spaces
• Fourier series and Fourier integrals
• Discrete and continuous probability distributions
• Analytic functions
• Laplace transforms
• Green's function

• Department of Physics, Indian Institute of Technology Madras, Chennai, India

  V. Balakrishnan

Prof. V. Balakrishnan is an Emeritus Professor of Physics at the Indian Institute of Technology (IIT) Madras. He joined the Indian Institute of Technology Madras as a Professor in 1980, and retired as Emeritus Professor in 2013. He was educated at the University of Delhi and received his PhD in theoretical physics from Brandeis University, USA 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 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 Non-equilibrium Statistical Mechanics. Over nearly four decades, he has taught a wide variety of extremely popular courses at the undergraduate, postgraduate and doctoral levels, comprising all the standard subjects in physics as well as some new and non-traditional ones. He has received high accolades for his teaching at IIT 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. He has held visiting positions at several institutions abroad. He is a Fellow of the Indian Academy of Sciences.

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