Tensors, Differential Forms, and Variational Principles (eBook)

David Lovelock, Hanno Rund (Autoren)

eBook Download: EPUB

2012
400 Seiten
Dover Publications (Verlag)
9780486131986 (ISBN)

Infos

Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.

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The aim of this book is to present a self-contained, reasonably modern account of tensor analysis and the calculus of exterior differential forms, adapted to the needs of physicists, engineers, and applied mathematicians. In the later, increasingly sophisticated chapters, the interaction between the concept of invariance and the calculus of variations is examined. This interaction is of profound importance to all physical field theories.Beginning with simple physical examples, the theory of tensors and forms is developed by a process of successive abstractions. This enables the reader to infer generalized principles from concrete situations — departing from the traditional approach to tensors and forms in terms of purely differential-geometric concepts.The treatment of the calculus of variations of single and multiple integrals is based ab initio on Carathéodory's method of equivalent integrals. Subsequent material explores the effects of invariance postulates on variational principles, focusing ultimately on relativistic field theories. Other discussions include:• integral invariants• simple and direct derivations of Noether's theorems• Riemannian spaces with indefinite metricsThe emphasis in this book is on analytical techniques, with abundant problems, ranging from routine manipulative exercises to technically difficult problems encountered by those using tensor techniques in research activities. A special effort has been made to collect many useful results of a technical nature, not generally discussed in the standard literature. The Appendix, newly revised and enlarged for the Dover edition, presents a reformulation of the principal concepts of the main text within the terminology of current global differential geometry, thus bridging the gap between classical tensor analysis and the fundamentals of more recent global theories.

Produkt-Details

• Erscheint lt. Verlag: 20.4.2012
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Maße: 140 x 140 mm
• Gewicht: 420 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Schlagworte: advanced physics • Analytical • books on advanced physics • books on boundary conditions • books on chaps • books on classical mechanics • books on configurations • books on curvatures • books on d'alemberts • books on derivations • books on derivatives • books on differential geometries • books on equations • books on euler • books on feynman • books on integrals • books on invariances • books on lagrange • books on lagrangians • books on manifolds • books on mathematical physics • books on notations • books on quantum mechanics • books on relativities • books on scalar • books on schutz • books on tensor analysis • books on tensor calculus • books on tensors • books on theorems • books on theoretical physics • books on variables • books on variations • books on vectors • Boundary conditions • Canonical • CHAP • classical mechanics • Configuration • Coordinates • Covariant • Curvature • D'Alembert • Derivation • Derivatives • Differential Geometry • Equations • euclidean • Euler • Feynman • hamiltonian • integrals • intuitive grasp • Invariance • Invariant • Lagrange • Lagrangian • Manifolds • Mathematical Physics • metric • Newtonian • Noether • Notation • quantum mechanics • Relativistic • Relativity • riemannian • scalar • Schutz • Tensor Analysis • tensor calculus • Tensors • Theorems • theoretical physics • Variables • Variations • Vectors
• ISBN-13: 9780486131986 / 9780486131986