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Cover Art
E-RESOURCE
Author Cortés, Vicente, 1965- author.

Title Mathematical methods of classical physics / Vicente Cortés, Alexander S. Haupt.

Published Cham, Switzerland : Springer, 2017.

Copies

Location Call No. Status
 UniM INTERNET resource    AVAILABLE
Physical description 1 online resource.
Series SpringerBriefs in physics
SpringerBriefs in physics.
Springer Physics and Astronomy eBooks 2017 English+International
Bibliography Includes bibliographical references and index.
Contents Acknowledgements; Contents; Symbols; 1 Introduction; 2 Lagrangian Mechanics; 2.1 Lagrangian Mechanical Systems and their Equations of Motion; 2.2 Integrals of Motion; 2.3 Motion in a Radial Potential; 2.3.1 Motion in Newton's Gravitational Potential; 3 Hamiltonian Mechanics; 3.1 Symplectic Geometry and Hamiltonian Systems; 3.2 Relation between Lagrangian and Hamiltonian Systems; 3.2.1 Hamiltonian Formulation for the Lagrangian Systems of Example 2.32.3; 3.2.2 The Legendre Transform; 3.3 Linearization and Stability; 4 Hamilton -- Jacobi Theory; 5 Classical Field Theory.
5.1 The Lagrangian, the Action and the Euler -- Lagrange Equations5.2 Automorphisms and Conservation Laws; 5.3 Why are Conservation Laws called Conservation Laws?; 5.4 Examples of Field Theories; 5.4.1 Sigma Models; 5.4.2 Pure Yang -- Mills Theory; 5.4.3 The Einstein -- Hilbert Lagrangian; 5.5 The Energy-Momentum Tensor; Appendix A Exercises; A.1 Exercises for Chap. 2; A.2 Exercises for Chap. 3; A.3 Exercises for Chap. 4; A.4 Exercises for Chap. 5; Appendix References; ; Index.
Summary This short primer, geared towards students with a strong interest in mathematically rigorous approaches, introduces the essentials of classical physics, briefly points out its place in the history of physics and its relation to modern physics, and explains what benefits can be gained from a mathematical perspective. As a starting point, Newtonian mechanics is introduced and its limitations are discussed. This leads to and motivates the study of different formulations of classical mechanics, such as Lagrangian and Hamiltonian mechanics, which are the subjects of later chapters. In the second part, a chapter on classical field theories introduces more advanced material. Numerous exercises are collected in the appendix.
Other author Haupt, Alexander S., author.
SpringerLink issuing body.
Subject Mathematical physics.
Electronic books.
ISBN 9783319564630 (electronic bk.)
3319564633 (electronic bk.)
9783319564623 (print)
3319564625
Standard Number 10.1007/978-3-319-56463-0