mathematical methods of classical mechanics graduate texts in mathematics

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Mathematical Methods Of Classical Mechanics

Author : V.I. Arnol'd
ISBN : 9781475720631
Genre : Mathematics
File Size : 71. 91 MB
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This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

Mathematical Methods Of Classical Mechanics

Author : V.I. Arnol'd
ISBN : 0387968903
Genre : Mathematics
File Size : 80. 45 MB
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This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

Mathematics Of Classical And Quantum Physics

Author : Frederick W. Byron
ISBN : 9780486135069
Genre : Science
File Size : 22. 51 MB
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Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.

Classical Mechanics

Author : Joseph L. McCauley
ISBN : 0521578825
Genre : Science
File Size : 37. 83 MB
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An advanced text for first-year graduate students in physics and engineering taking a standard classical mechanics course, this is the first book to describe the subject in the context of the language and methods of modern nonlinear dynamics. The organizing principle of the text is integrability vs. nonintegrability. It introduces flows in phase space and transformations early and illustrates their applications throughout the text. The standard integrable problems of elementary physics are analyzed from the standpoint of flows, transformations, and integrability. This approach allows the author to introduce most of the interesting ideas of modern nonlinear dynamics via the most elementary nonintegrable problems of Newtonian mechanics. This text will also interest specialists in nonlinear dynamics, mathematicians, engineers and system theorists.

Quantum Mechanics For Mathematicians

Author : Leon Armenovich Takhtadzhi͡an
ISBN : 9780821846308
Genre : Mathematics
File Size : 20. 98 MB
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This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with second-year graduate students. It addition to traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin, and it introduces the reader to functional methods in quantum mechanics. This includes the Feynman path integral approach to quantum mechanics, integration in functional spaces, the relation between Feynman and Wiener integrals, Gaussian integration and regularized determinants of differential operators, fermion systems and integration over anticommuting (Grassmann) variables, supersymmetry and localization in loop spaces, and supersymmetric derivation of the Atiyah-Singer formula for the index of the Dirac operator. Prior to this book, mathematicians could find these topics only in physics textbooks and in specialized literature. This book is written in a concise style with careful attention to precise mathematics formulation of methods and results.Numerous problems, from routine to advanced, help the reader to master the subject. In addition to providing a fundamental knowledge of quantum mechanics, this book could also serve as a bridge for studying more advanced topics in quantum physics, among them quantum field theory. Prerequisites include standard first-year graduate courses covering linear and abstract algebra, topology and geometry, and real and complex analysis.

Applications Of Lie Groups To Differential Equations

Author : Peter J. Olver
ISBN : 9781468402742
Genre : Mathematics
File Size : 46. 36 MB
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This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.

Structure And Interpretation Of Classical Mechanics

Author : Gerald Jay Sussman
ISBN : 9780262028967
Genre : Science
File Size : 64. 66 MB
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The new edition of a classic text that concentrates on developing general methods for studying the behavior of classical systems, with extensive use of computation.

Introduction To Dynamics

Author : I. C. Percival
ISBN : 0521281490
Genre : Mathematics
File Size : 42. 13 MB
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A new approach to dynamics that takes account of recent advances that have wide applications in the sciences and engineering. It introduces the subject at an undergraduate level by means of elementary qualitative theory of differential equations, the geometry of phase curves, and the theory of stability.

Arnold S Problems

Author : Vladimir I. Arnold
ISBN : 3540206140
Genre : Mathematics
File Size : 83. 95 MB
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Vladimir Arnold is one of the most outstanding mathematicians of our time Many of these problems are at the front line of current research

Physics For Mathematicians

Author : Michael Spivak
ISBN : 0914098322
Genre : Mechanics
File Size : 83. 24 MB
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