Special Matrices Of Mathematical Physics
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| Author | : Ruben Aldrovandi |
| Publisher | : World Scientific |
| Total Pages | : 344 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 9789812799838 |
Ch. 1. Some fundamental notions. 1.1. Definitions. 1.2. Components of a matrix. 1.3. Matrix functions. 1.4. Normal matrices -- ch. 2. Evolving systems -- ch. 3. Markov chains. 3.1. Non-negative matrices. 3.2. General properties -- ch. 4. Glass transition -- ch. 5. The Kerner model. 5.1. A simple example: Se-As glass -- ch. 6. Formal developments. 6.1. Spectral aspects. 6.2. Reducibility and regularity. 6.3. Projectors and asymptotics. 6.4. Continuum time -- ch. 7. Equilibrium, dissipation and ergodicity. 7.1. Recurrence, transience and periodicity. 7.2. Detailed balancing and reversibility. 7.3. Ergodicity -- ch. 8. Prelude -- ch. 9. Definition and main properties. 9.1. Bases. 9.2. Double Fourier transform. 9.3. Random walks -- ch. 10. Discrete quantum mechanics. 10.1. Introduction. 10.2. Weyl-Heisenberg groups. 10.3. Weyl-Wigner transformations. 10.4. Braiding and quantum groups -- ch. 11. Quantum symplectic structure. 11.1. Matrix differential geometry. 11.2. The symplectic form. 11.3. The quantum fabric -- ch. 12. An organizing tool -- ch. 13. Bell polynomials. 13.1. Definition and elementary properties. 13.2. The matrix representation. 13.3. The Lagrange inversion formula. 13.4. Developments -- ch. 14. Determinants and traces. 14.1. Introduction. 14.2. Symmetric functions. 14.3. Polynomials. 14.4. Characteristic polynomials. 14.5. Lie algebras invariants -- ch. 15. Projectors and iterates. 15.1. Projectors, revisited. 15.2. Continuous iterates -- ch. 16. Gases: real and ideal. 16.1. Microcanonical ensemble. 16.2. The canonical ensemble. 16.3. The grand canonical ensemble. 16.4. Braid statistics. 16.5. Condensation theories. 16.6. The Fredholm formalism.
| Author | : Gupta B.D. |
| Publisher | : Vikas Publishing House |
| Total Pages | : 1448 |
| Release | : 2021 |
| Genre | : Science |
| ISBN | : 8125930965 |
Mathematics is an essential ingredient in the education of a student of mathematics or physics of a professional physicist, indeed in the education of any professional scientist or engineer. The purpose of Mathematical Physics is to provide a comprehensive study of the mathematics underlying theoretical physics at the level of graduate and postgraduate students and also have enough depth for others interested in higher level mathematics relevant to specialized fields. It is also intended to serve the research scientist or engineer who needs a quick refresher course in the subject. The Fourth Edition of the book has been thoroughly revised and updated keeping in mind the requirements of students and the latest UGC syllabus.
| 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 | : Feliks Ruvimovich Gantmakher |
| Publisher | : |
| Total Pages | : 296 |
| Release | : 1960 |
| Genre | : Matrices |
| ISBN | : |
| 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.
| Author | : Ruben Aldrovandi |
| Publisher | : World Scientific |
| Total Pages | : 340 |
| Release | : 2001 |
| Genre | : Science |
| ISBN | : 9810247087 |
This book expounds three special kinds of matrices that are of physical interest, centering on physical examples. Stochastic matrices describe dynamical systems of many different types, involving (or not) phenomena like transience, dissipation, ergodicity, nonequilibrium, and hypersensitivity to initial conditions. The main characteristic is growth by agglomeration, as in glass formation. Circulants are the building blocks of elementary Fourier analysis and provide a natural gateway to quantum mechanics and noncommutative geometry. Bell polynomials offer closed expressions for many formulas concerning Lie algebra invariants, differential geometry and real gases, and their matrices are instrumental in the study of chaotic mappings.
| Author | : Aldrovandi Ruben |
| Publisher | : World Scientific |
| Total Pages | : 844 |
| Release | : 2016-10-07 |
| Genre | : Science |
| ISBN | : 9813146834 |
This book focuses on the unifying power of the geometrical language in bringing together concepts from many different areas of physics, ranging from classical physics to the theories describing the four fundamental interactions of Nature -- gravitational, electromagnetic, strong nuclear, and weak nuclear. The book provides in a single volume a thorough introduction to topology and differential geometry, as well as many applications to both mathematical and physical problems. It is aimed as an elementary text and is intended for first year graduate students. In addition to the traditional contents of books on special and general relativities, this book discusses also some recent advances such as de Sitter invariant special relativity, teleparallel gravity and their implications in cosmology for those wishing to reach a higher level of understanding.
| Author | : Chun Wa Wong |
| Publisher | : OUP Oxford |
| Total Pages | : 731 |
| Release | : 2013-01-24 |
| Genre | : Science |
| ISBN | : 0191648604 |
Mathematical physics provides physical theories with their logical basis and the tools for drawing conclusions from hypotheses. Introduction to Mathematical Physics explains to the reader why and how mathematics is needed in the description of physical events in space. For undergraduates in physics, it is a classroom-tested textbook on vector analysis, linear operators, Fourier series and integrals, differential equations, special functions and functions of a complex variable. Strongly correlated with core undergraduate courses on classical and quantum mechanics and electromagnetism, it helps the student master these necessary mathematical skills. It contains advanced topics of interest to graduate students on relativistic square-root spaces and nonlinear systems. It contains many tables of mathematical formulas and references to useful materials on the Internet. It includes short tutorials on basic mathematical topics to help readers refresh their mathematical knowledge. An appendix on Mathematica encourages the reader to use computer-aided algebra to solve problems in mathematical physics. A free Instructor's Solutions Manual is available to instructors who order the book for course adoption.
| Author | : Michael Spivak |
| Publisher | : |
| Total Pages | : 733 |
| Release | : 2010 |
| Genre | : Mechanics |
| ISBN | : 9780914098324 |
| Author | : Dennis S. Bernstein |
| Publisher | : Princeton University Press |
| Total Pages | : 1183 |
| Release | : 2009-07-26 |
| Genre | : Mathematics |
| ISBN | : 0691140391 |
Each chapter in this book describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly with cross references, citations to the literature, and illuminating remarks.
