Geometry, symmetries, and classical physics : a mosaic / Manousos Markoutsakis.

Includes bibliographical references and index.

Part I: Geometric manifolds -- Manifolds and tensors -- Geometry and integration on manifolds -- Symmetries of manifolds -- Part II: Mechanics and symmetry -- Newtonian mechanics -- Lagrangian methods and symmetry -- Relativistic mechanics -- Part III: Symmetry groups and algebras -- Lie groups -- Lie algebras -- Representations -- Rotations and Euclidean symmetry -- Boosts and Galilei symmetry -- Lorentz symmetry -- Poincaré symmetry -- Conformal symmetry -- Part IV: Classical fields -- Lagrangians and Noether's theorem -- Spacetime symmetries of fields -- Gauge symmetry -- Part V: Riemannian geometry -- Connection and geodesics -- Riemannian curvature -- Symmetries of Riemannian manifolds -- Part VI: General relativity and symmetry -- Einstein's gravitation -- Lagrangian formulation -- Conservation laws and further symmetries -- Part VII: Appendices -- Notation and conventions -- Mathematical tools -- Weyl rescaling formulae -- Spaces and symmetry groups.

"This book provides advanced undergraduate physics and mathematics students with an accessible yet detailed understanding of the fundamentals of differential geometry and symmetries in classical physics. Readers, working through the book, will obtain a thorough understanding of symmetry principles and their application in mechanics, field theory, and general relativity, and in addition acquire the necessary calculational skills to tackle more sophisticated questions in theoretical physics. Most of the topics covered in this book have previously only been scattered across many different sources of literature, therefore this is the first book to coherently present this treatment of topics in one comprehensive volume." -- Provided by publisher