Ebook: 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.

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This book combines the enlarged and corrected editions of both volumes on classical physics of Thirring's famous course in mathematical physics. With numerous examples and remarks complementing the text, it is suitable as a textbook for students of physics, mathematics, and applied mathematics. The treatment of classical dynamical systems employs analysis on manifolds to provide the mathematical setting for discussions of Hamiltonian systems; problems discussed in detail include nonrelativistic motion of particles and systems, relativis- tic motion in electromagnetic and gravitational fields, and the structure of black holes. The treatment of classical fields used differential geometry to examine both Maxwell's and Einstein's equations with new material added on gauge theories.

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This book combines the enlarged and corrected editions of both volumes on classical physics of Thirring's famous course in mathematical physics. With numerous examples and remarks complementing the text, it is suitable as a textbook for students of physics, mathematics, and applied mathematics. The treatment of classical dynamical systems employs analysis on manifolds to provide the mathematical setting for discussions of Hamiltonian systems; problems discussed in detail include nonrelativistic motion of particles and systems, relativis- tic motion in electromagnetic and gravitational fields, and the structure of black holes. The treatment of classical fields used differential geometry to examine both Maxwell's and Einstein's equations with new material added on gauge theories.
Content:
Front Matter....Pages i-xxviii
Introduction....Pages 1-7
Analysis on Manifolds....Pages 8-83
Hamiltonian Systems....Pages 84-164
Nonrelativistic Motion....Pages 165-209
Relativistic Motion....Pages 210-261
The Structure of Space and Time....Pages 262-278
Introduction....Pages 279-323
The Electromagnetic Field of a Known Charge Distribution....Pages 324-379
The Field in the Presence of Conductors....Pages 380-432
Gravitation....Pages 433-530
Back Matter....Pages 531-547

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This book combines the enlarged and corrected editions of both volumes on classical physics of Thirring's famous course in mathematical physics. With numerous examples and remarks complementing the text, it is suitable as a textbook for students of physics, mathematics, and applied mathematics. The treatment of classical dynamical systems employs analysis on manifolds to provide the mathematical setting for discussions of Hamiltonian systems; problems discussed in detail include nonrelativistic motion of particles and systems, relativis- tic motion in electromagnetic and gravitational fields, and the structure of black holes. The treatment of classical fields used differential geometry to examine both Maxwell's and Einstein's equations with new material added on gauge theories.
Content:
Front Matter....Pages i-xxviii
Introduction....Pages 1-7
Analysis on Manifolds....Pages 8-83
Hamiltonian Systems....Pages 84-164
Nonrelativistic Motion....Pages 165-209
Relativistic Motion....Pages 210-261
The Structure of Space and Time....Pages 262-278
Introduction....Pages 279-323
The Electromagnetic Field of a Known Charge Distribution....Pages 324-379
The Field in the Presence of Conductors....Pages 380-432
Gravitation....Pages 433-530
Back Matter....Pages 531-547
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