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Mathematical Physics Classical Mechanics

Author: Andreas Knauf
Publisher: Springer
ISBN: 3662557746
Size: 38.47 MB
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As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics. The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.

Mathematical Methods Of Classical Mechanics

Author: V.I. Arnol'd
Publisher: Springer Science & Business Media
ISBN: 1475720637
Size: 10.68 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 Physics

Author: Donald H. Menzel
Publisher: Courier Corporation
ISBN: 0486139107
Size: 40.94 MB
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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.

Classical Mechanics

Author: Emmanuele DiBenedetto
Publisher: Springer Science & Business Media
ISBN: 9780817646486
Size: 58.42 MB
Format: PDF
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* Offers a rigorous mathematical treatment of mechanics as a text or reference * Revisits beautiful classical material, including gyroscopes, precessions, spinning tops, effects of rotation of the Earth on gravity motions, and variational principles * Employs mathematics not only as a "unifying" language, but also to exemplify its role as a catalyst behind new concepts and discoveries

Mathematics Of Classical And Quantum Physics

Author: Frederick W. Byron
Publisher: Courier Corporation
ISBN: 0486135063
Size: 70.76 MB
Format: PDF, ePub
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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.

Mathematical Physics I

Author: Matteo Petrera
ISBN: 9783832535698
Size: 21.25 MB
Format: PDF
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These Lecture Notes provide an introduction to the theory of finite-dimensional dynamical systems. The first part presents the main classical results about continuous time dynamical systems with a finite number of degrees of freedom. Among the topics covered are: initial value problems, geometrical methods in the theory of ordinary differential equations, stability theory, aspects of local bifurcation theory. The second part is devoted to the Lagrangian and Hamiltonian formulation of finite-dimensional dynamical systems, both on Euclidean spaces and smooth manifolds. The main topics are: variational formulation of Newtonian mechanics, canonical Hamiltonian mechanics, theory of canonical transformations, introduction to mechanics on Poisson and symplectic manifolds. The material is presented in a way that is at once intuitive, systematic and mathematically rigorous. The theoretical part is supplemented with many concrete examples and exercises.

Mathematical Methods In Classical And Quantum Physics

Author: Tulsi Dass
Publisher: Universities Press
ISBN: 9788173710896
Size: 42.59 MB
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This book is intended to provide an adequate background for various theortical physics courses, especially those in classical mechanics, electrodynamics, quatum mechanics and statistical physics. Each topic is dealt with in a generally self-contained manner and the text is interspersed with a number of solved examples ad a large number of exercise problems.

Partial Differential Equations In Classical Mathematical Physics

Author: Isaak Rubinstein
Publisher: Cambridge University Press
ISBN: 9780521558464
Size: 41.61 MB
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This book considers the theory of partial differential equations as the language of continuous processes in mathematical physics. This is an interdisciplinary area in which the mathematical phenomena are reflections of their physical counterparts. The authors trace the development of these mathematical phenomena in different natural sciences, with examples drawn from continuum mechanics, electrodynamics, transport phenomena, thermodynamics, and chemical kinetics. At the same time, the authors trace the interrelation between the different types of problems--elliptic, parabolic, and hyperbolic--as the mathematical counterparts of stationary and evolutionary processes. This combination of mathematical comprehensiveness and natural scientific motivation represents a step forward in the presentation of the classical theory of PDEs, one that will be appreciated by students and researchers in applied mathematics and mathematical physics.

Classical Mechanics With Mathematica

Author: Antonio Romano
Publisher: Springer Science & Business Media
ISBN: 0817683526
Size: 56.94 MB
Format: PDF, Docs
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This textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject.​ Developed by the author from 35 years of teaching experience, the presentation is designed to give students an overview of the many different models used through the history of the field—from Newton to Lagrange—while also painting a clear picture of the most modern developments. Throughout, it makes heavy use of the powerful tools offered by Mathematica​. The volume is organized into two parts. The first focuses on developing the mathematical framework of linear algebra and differential geometry necessary for the remainder of the book. Topics covered include tensor algebra, Euclidean and symplectic vector spaces, differential manifolds, and absolute differential calculus. The second part of the book applies these topics to kinematics, rigid body dynamics, Lagrangian and Hamiltonian dynamics, Hamilton–Jacobi theory, completely integrable systems, statistical mechanics of equilibrium, and impulsive dynamics, among others. Unique in its scope of coverage and method of approach, Classical Mechanics will be a very useful resource for graduate students and advanced undergraduates in applied mathematics and physics who hope to gain a deeper understanding of mechanics.