A Course in Mathematical Physics 1 and 2: Classical Dynamical Systems and Classical Field Theory

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9780387976099: A Course in Mathematical Physics 1 and 2: Classical Dynamical Systems and Classical Field Theory

The last decade has seen a considerable renaissance in the realm of classical dynamical systems, and many things that may have appeared mathematically overly sophisticated at the time of the first appearance of this textbook have since become the everyday tools of working physicists. This new edition is intended to take this development into account. I have also tried to make the book more readable and to eradicate errors. Since the first edition already contained plenty of material for a one- semester course, new material was added only when some of the original could be dropped or simplified. Even so, it was necessary to expand the chap- ter with the proof of the K-A-M Theorem to make allowances for the cur- rent trend in physics. This involved not only the use of more refined mathe- matical tools, but also a reevaluation of the word "fundamental. " What was earlier dismissed as a grubby calculation is now seen as the consequence of a deep principle. Even Kepler's laws, which determine the radii of the planetary orbits, and which used to be passed over in silence as mystical nonsense, seem to point the way to a truth unattainable by superficial observation: The ratios of the radii of Platonic solids to the radii of inscribed Platonic solids are irrational, but satisfy algebraic equations of lower order.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Contenuti:

1 Introduction.- 1.1 Equations of Motion.- 1.2 The Mathematical Language.- 1.3 The Physical Interpretation.- 2 Analysis on Manifolds.- 2.1 Manifolds.- 2.2 Tangent Spaces.- 2.3 Flows.- 2.4 Tensors.- 2.5 Differentiation.- 2.6 Integrals.- 3 Hamiltonian Systems.- 3.1 Canonical Transformations g.- 3.2 Hamilton’s Equations.- 3.3 Constants of Motion.- 3.4 The Limit t ? I ± ?.- 3.5 Perturbation Theory: Preliminaries.- 3.6 Perturbation Theory: The Iteration.- 4 Nonrelativistic Motion.- 4.1 Free Particles.- 4.2 The Two-Body Problem.- 4.3 The Problem of Two Centers of Force.- 4.4 The Restricted Three-Body Problem.- 4.5 The N-body Problem.- 5 Relativistic Motion.- 5.1 The Hamiltonian Formulation of the Electrodynamic Equations of Motions.- 5.2 The Constant Field.- 5.3 The Coulomb Field.- 5.4 The Betatron.- 5.5 The Traveling Plane Disturbance.- 5.6 Relativistic Motion in a Gravitational Field.- 5.7 Motion in the Schwarzschild Field.- 5.8 Motion in a Gravitational Plane Wave.- 6 The Structure of Space and Time.- 6.1 The Homogeneous Universe.- 6.2 The Isotropic Universe.- 6.3 Me according to Galileo.- 6.4 Me as Minkowski Space.- 6.5 Me as a Pseudo-Riemannian Space.- 1. Introduction.- 1.1 Physical Aspects of Field Dynamics.- 1.2 The Mathematical Formalism.- 1.3 Maxwell’s and Einstein’s Equations.- 2. The Electromagnetic Field of a Known Charge Distribution.- 2.1 The Stationary-Action Principle and Conservation Theorems.- 2.2 The General Solution.- 2.3 The Field of a Point Charge.- 2.4 Radiative Reaction.- 3. The Field in the Presence of Conductors.- 3.1 The Superconductor.- 3.2 The Half-Space, the Wave-Guide, and the Resonant Cavity.- 3.3 Diffraction at a Wedge.- 3.4 Diffraction at a Cylinder.- 4. Gravitation.- 4.1 Covariant Differentiation and the Curvature of Space.- 4.2 Gauge Theories and Gravitation.- 4.3 Maximally Symmetric Spaces.- 4.4 Spaces with Maximally Symmetric Submanifolds.- 4.5 The Life and Death of Stars.- 4.6 The Existence of Singularities.

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Thirring, Walter
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Descrizione libro Springer, 1991. Paperback. Condizione libro: New. book. Codice libro della libreria 0387976094

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Descrizione libro Springer-Verlag New York Inc., United States, 1992. Paperback. Condizione libro: New. 229 x 152 mm. Language: English . Brand New Book ***** Print on Demand *****.The last decade has seen a considerable renaissance in the realm of classical dynamical systems, and many things that may have appeared mathematically overly sophisticated at the time of the first appearance of this textbook have since become the everyday tools of working physicists. This new edition is intended to take this development into account. I have also tried to make the book more readable and to eradicate errors. Since the first edition already contained plenty of material for a one- semester course, new material was added only when some of the original could be dropped or simplified. Even so, it was necessary to expand the chap- ter with the proof of the K-A-M Theorem to make allowances for the cur- rent trend in physics. This involved not only the use of more refined mathe- matical tools, but also a reevaluation of the word fundamental. What was earlier dismissed as a grubby calculation is now seen as the consequence of a deep principle. Even Kepler s laws, which determine the radii of the planetary orbits, and which used to be passed over in silence as mystical nonsense, seem to point the way to a truth unattainable by superficial observation: The ratios of the radii of Platonic solids to the radii of inscribed Platonic solids are irrational, but satisfy algebraic equations of lower order. Softcover reprint of the original 2nd ed. 1992. Codice libro della libreria AAV9780387976099

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Walter E. Thirring
Editore: Springer-Verlag New York Inc., United States (1992)
ISBN 10: 0387976094 ISBN 13: 9780387976099
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Descrizione libro Springer-Verlag New York Inc., United States, 1992. Paperback. Condizione libro: New. 229 x 152 mm. Language: English . Brand New Book ***** Print on Demand *****. The last decade has seen a considerable renaissance in the realm of classical dynamical systems, and many things that may have appeared mathematically overly sophisticated at the time of the first appearance of this textbook have since become the everyday tools of working physicists. This new edition is intended to take this development into account. I have also tried to make the book more readable and to eradicate errors. Since the first edition already contained plenty of material for a one- semester course, new material was added only when some of the original could be dropped or simplified. Even so, it was necessary to expand the chap- ter with the proof of the K-A-M Theorem to make allowances for the cur- rent trend in physics. This involved not only the use of more refined mathe- matical tools, but also a reevaluation of the word fundamental. What was earlier dismissed as a grubby calculation is now seen as the consequence of a deep principle. Even Kepler s laws, which determine the radii of the planetary orbits, and which used to be passed over in silence as mystical nonsense, seem to point the way to a truth unattainable by superficial observation: The ratios of the radii of Platonic solids to the radii of inscribed Platonic solids are irrational, but satisfy algebraic equations of lower order. Softcover reprint of the original 2nd ed. 1992. Codice libro della libreria AAV9780387976099

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Walter E. Thirring
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Descrizione libro Springer-Verlag New York Inc., 1991. PAP. Condizione libro: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria LQ-9780387976099

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Descrizione libro Springer, 1991. Paperback. Condizione libro: NEW. 9780387976099 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0276446

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Descrizione libro Springer, 1991. Paperback. Condizione libro: New. Softcover reprint of the origina. This item is printed on demand. Codice libro della libreria DADAX0387976094

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