Mathematical Physics Ii
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Author | : Enrico De Micheli |
Publisher | : MDPI |
Total Pages | : 182 |
Release | : 2020-12-15 |
Genre | : Mathematics |
ISBN | : 3039434950 |
The charm of Mathematical Physics resides in the conceptual difficulty of understanding why the language of Mathematics is so appropriate to formulate the laws of Physics and to make precise predictions. Citing Eugene Wigner, this “unreasonable appropriateness of Mathematics in the Natural Sciences” emerged soon at the beginning of the scientific thought and was splendidly depicted by the words of Galileo: “The grand book, the Universe, is written in the language of Mathematics.” In this marriage, what Bertrand Russell called the supreme beauty, cold and austere, of Mathematics complements the supreme beauty, warm and engaging, of Physics. This book, which consists of nine articles, gives a flavor of these beauties and covers an ample range of mathematical subjects that play a relevant role in the study of physics and engineering. This range includes the study of free probability measures associated with p-adic number fields, non-commutative measures of quantum discord, non-linear Schrödinger equation analysis, spectral operators related to holomorphic extensions of series expansions, Gibbs phenomenon, deformed wave equation analysis, and optimization methods in the numerical study of material properties.
Author | : Richard Courant |
Publisher | : |
Total Pages | : 830 |
Release | : 1965 |
Genre | : |
ISBN | : |
Author | : Donald H. Menzel |
Publisher | : Courier Corporation |
Total Pages | : 434 |
Release | : 2012-05-23 |
Genre | : Science |
ISBN | : 0486139107 |
Useful treatment of classical mechanics, electromagnetic theory, and relativity includes explanations of function theory, vectors, matrices, dyadics, tensors, partial differential equations, other advanced mathematical techniques. Nearly 200 problems with answers.
Author | : Wolfgang Nolting |
Publisher | : Springer |
Total Pages | : 367 |
Release | : 2016-06-28 |
Genre | : Science |
ISBN | : 3319401297 |
This textbook offers a clear and comprehensive introduction to analytical mechanics, one of the core components of undergraduate physics courses. The book starts with a thorough introduction into Lagrangian mechanics, detailing the d’Alembert principle, Hamilton’s principle and conservation laws. It continues with an in-depth explanation of Hamiltonian mechanics, illustrated by canonical and Legendre transformation, the generalization to quantum mechanics through Poisson brackets and all relevant variational principles. Finally, the Hamilton-Jacobi theory and the transition to wave mechanics are presented in detail. Ideally suited to undergraduate students with some grounding in classical mechanics, the book is enhanced throughout with learning features such as boxed inserts and chapter summaries, with key mathematical derivations highlighted to aid understanding. The text is supported by numerous worked examples and end of chapter problem sets. About the Theoretical Physics series Translated from the renowned and highly successful German editions, the eight volumes of this series cover the complete core curriculum of theoretical physics at undergraduate level. Each volume is self-contained and provides all the material necessary for the individual course topic. Numerous problems with detailed solutions support a deeper understanding. Wolfgang Nolting is famous for his refined didactical style and has been referred to as the "German Feynman" in reviews.
Author | : R.D. Richtmyer |
Publisher | : Springer Science & Business Media |
Total Pages | : 332 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 3642510760 |
Author | : Sadri Hassani |
Publisher | : Springer Science & Business Media |
Total Pages | : 1052 |
Release | : 2002-02-08 |
Genre | : Science |
ISBN | : 9780387985794 |
For physics students interested in the mathematics they use, and for math students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation strikes a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained.
Author | : Michael Spivak |
Publisher | : |
Total Pages | : 733 |
Release | : 2010 |
Genre | : Mechanics |
ISBN | : 9780914098324 |
Author | : R. Shankar |
Publisher | : Yale University Press |
Total Pages | : 609 |
Release | : 2016-01-01 |
Genre | : Science |
ISBN | : 0300212364 |
Explains the fundamental concepts of Newtonian mechanics, special relativity, waves, fluids, thermodynamics, and statistical mechanics. Provides an introduction for college-level students of physics, chemistry, and engineering, for AP Physics students, and for general readers interested in advances in the sciences. In volume II, Shankar explains essential concepts, including electromagnetism, optics, and quantum mechanics. The book begins at the simplest level, develops the basics, and reinforces fundamentals, ensuring a solid foundation in the principles and methods of physics.
Author | : Harry Hochstadt |
Publisher | : Courier Corporation |
Total Pages | : 354 |
Release | : 2012-04-30 |
Genre | : Science |
ISBN | : 0486168786 |
A modern classic, this clearly written, incisive textbook provides a comprehensive, detailed survey of the functions of mathematical physics, a field of study straddling the somewhat artificial boundary between pure and applied mathematics. In the 18th and 19th centuries, the theorists who devoted themselves to this field — pioneers such as Gauss, Euler, Fourier, Legendre, and Bessel — were searching for mathematical solutions to physical problems. Today, although most of the functions have practical applications, in areas ranging from the quantum-theoretical model of the atom to the vibrating membrane, some, such as those related to the theory of discontinuous groups, still remain of purely mathematical interest. Chapters One and Two examine orthogonal polynomials, with sections on such topics as the recurrence formula, the Christoffel-Darboux formula, the Weierstrass approximation theorem, and the application of Hermite polynomials to quantum mechanics. Chapter Three is devoted to the principal properties of the gamma function, including asymptotic expansions and Mellin-Barnes integrals. Chapter Four covers hypergeometric functions, including a review of linear differential equations with regular singular points, and a general method for finding integral representations. Chapters Five and Six are concerned with the Legendre functions and their use in the solutions of Laplace's equation in spherical coordinates, as well as problems in an n-dimension setting. Chapter Seven deals with confluent hypergeometric functions, and Chapter Eight examines, at length, the most important of these — the Bessel functions. Chapter Nine covers Hill's equations, including the expansion theorems.
Author | : Peter Szekeres |
Publisher | : Cambridge University Press |
Total Pages | : 620 |
Release | : 2004-12-16 |
Genre | : Mathematics |
ISBN | : 9780521829601 |
This textbook, first published in 2004, provides an introduction to the major mathematical structures used in physics today.