عنوان

Mathematical methods of classical physics

3319564625

9783319564623

b389721

Mathematical methods of classical physics

[Book]

Vicente Cortés, Alexander S. Haupt.

Cham, Switzerland

Springer,

2017.

xi, 99 pages : illustrations ; 24 cm

SpringerBriefs in physics.

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

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 leadsThis 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 leadsThis 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",,,,,"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.

Vicente Cortés

Alexander S Haupt

[Book]

Y