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Mathematical Physics de V. Balakrishnan

Mathematical Physics

Autor V. Balakrishnan
en Limba Engleză Hardback – 8 apr 2020
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. 

 
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Specificații

ISBN-13: 9783030396794
ISBN-10: 3030396797
Pagini: 812
Ilustrații: XXVII, 781 p. 137 illus., 1 illus. in color.
Dimensiuni: 160 x 241 x 46 mm
Greutate: 1.46 kg
Ediția:1st ed. 2020
Editura: Springer
Locul publicării:Cham, Switzerland

Cuprins

Chapter 1: Warming up: Functions of a real variable.- Chapter 2: Gaussian integrals, Stirling's formula, and some integrals.- Chapter 3: Some more functions.- Chapter 4: Generalized functions.- Chapter 5: Vectors and tensors.- Chapter 6: Vector calculus.- Chapter 7: A bit of 
fluid dynamics.- Chapter 8: Some more vector calculus.- Chapter 9: A bit of electromagnetism and special relativity.- Chapter 10: Linear vector spaces.- Chapter 11: A look at matrices.- Chapter 12: More about matrices.- Chapter 13: Infinite-dimensional vector spaces.- Chapter 14: Linear operators on a vector space.- Chapter 15: Operator algebras and identities.- Chapter 16: Orthogonal polynomials.- Chapter 17: Fourier series.- Chapter 18: Fourier integrals.- Chapter 19: Discrete probability distributions.- Chapter 20: Continuous probability distributions.- Chapter 21: Stochastic processes.- Chapter 22: Analytic functions of a complex variable.- Chapter 23: More on analytic functions.- Chapter 24: Linear response and analyticity.- Chapter 25: Analytic continuation and the gamma function.- Chapter 26: Multivalued functions and integral representations.- Chapter 27: Mobius transformations.- Chapter 28: Laplace transforms.- Chapter 29: Green function for the Laplacian operator.- Chapter 30: The diffusion equation.- Chapter 31: The wave equation.- Chapter 32: Integral equations.

Notă biografică

S. Lakshmibala earned her Ph. D. degree in theoretical high energy physics from the University of Madras in 1987 and joined the Department of Physics, IIT Madras, as a postdoctoral fellow. She became a faculty member in 1991 and is currently a professor there. Her research has ranged over particle physics, nonlinear dynamics, and the interface between quantum mechanics and quantum optics. For the past two decades, her research has focused on the general theme of the ergodic properties of the expectation values of observables in quantum mechanical systems, particularly in the context of paradigmatic atom-field interaction models in quantum optics. In addition to significant work in this area, she has also pioneered the application of time series and network analysis to quantum dynamics. She has taught a variety of courses at the undergraduate and graduate levels and has also given an NPTEL-sponsored video course on quantum mechanics (available on YouTube) that has been very well received. Among her current research interests is the tomographic approach to the exploration of entanglement in bipartite and multipartite systems. V. Balakrishnan earned his Ph. D. degree in theoretical high energy physics from Brandeis University in 1970. After a decade of research at TIFR (Mumbai) and IGCAR (Kalpakkam), he joined IIT Madras in 1980 as a professor, retired as professor emeritus in 2013, and is currently an adjunct professor there. His research interests have spanned many areas over the years, including particle physics, mechanical behavior of solids, condensed matter physics, random walks and stochastic processes, nonlinear dynamics and chaos, and quantum dynamics, in which he has published numerous research papers and articles. He has made significant contributions to the theory of an elasticity and viscoelasticity, anomalous diffusion and continuous time random walks, first-passage times for random walks on fractals, and extreme-value and recurrence-time distributions in chaotic dynamics. He is a co-author of Beyond the Crystalline State (Springer, 1989) and the author of Elements of Nonequilibrium Statistical Mechanics (Ane Books, 2008; Springer, 2021), Mathematical Physics (Ane Books, 2018; Springer, 2020) and A Miscellany of Mathematical Physics (Indian Academy of Sciences, 2018). Over four decades, he has taught a wide variety of extremely popular courses at the undergraduate and graduate levels. He has given seven NPTEL-sponsored video courses (available on YouTube). These have received very high acclaim, with a total of several million views worldwide. He has been a fellow of the Indian Academy of Sciences since 1985.

Textul de pe ultima copertă

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. 

 

Caracteristici

Covers a wide range of essential mathematical concepts useful for theoretical physics Provides physical applications of the mathematical techniques wherever possible Includes nearly 400 worked-out problems and end-of-chapter exercises