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The Geometry of Physics [Elektronisk resurs] An Introduction.
- Frankel, Theodore. (författare)
- ISBN 9781139159692
- 3rd ed.
- Publicerad: Cambridge : Cambridge University Press, 2011
- Engelska 1 online resource (750 p.)
- E-bok
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- Cover; The Geometry of Physics; Title; Copyright; ForThom-kat, Mont, Dave and Jonnie and In fond memory of Raoul Bott 1923-2005; Contents; Preface to the Third Edition; Preface to the Second Edition; Preface to the Revised Printing; Preface to the First Edition; OVERVIEW:An Informal Overview of Cartan's Exterior Differential Forms, Illustrated with an Application to Cauchy's Stress Tensor; Introduction; O.a. Introduction; Vectors, 1-Forms, and Tensors; O.b. Two Kinds of Vectors; O.c. Superscripts, Subscripts, Summation Convention; O.d. Riemannian Metrics; O.e. Tensors.
- Integrals and Exterior FormsO.f. Line Integrals; O.g. Exterior 2-Forms; O.h. Exterior p-Forms and Algebra in Rn; O.i. The Exterior Differential d; O.j. The Push-Forward of a Vector and the Pull-Back of a Form; O.k. Surface Integrals and "Stokes' theorem"; O.l. Electromagnetism, or, Is it a Vector or a Form?; O.m. Interior Products; O.n. Volume Forms and Cartan's Vector Valued Exterior Forms; O.o. Magnetic Field for Current in a Straight Wire; Elasticity and Stresses; O.p. Cauchy Stress, Floating Bodies, Twisted Cylinders,and Strain Energy; O.q. Sketch of Cauchy's "First Theorem".
- O.r. Sketch of Cauchy's "Second Theorem," Moments as Generators of RotationsO.s. A Remarkable Formula for Differentiating Line,Surface, and . . ., Integrals; PART ONE; Manifolds, Tensors, and Exterior Forms; CHAPTER 1; Manifolds and Vector Fields; 1.1. Submanifolds of Euclidean Space; 1.1a. Submanifolds of RN; 1.1b. The Geometry of Jacobian Matrices: The "Differential"; 1.1c. The Main Theorem on Submanifolds of RN; 1.1d. A Nontrivial Example: The Configuration Space of a Rigid Body; 1.2. Manifolds; 1.2a. Some Notions from Point Set Topology; 1.2b. The Idea of a Manifold.
- 1.2c. A Rigorous Definition of a Manifold1.2d. Complex Manifolds: The Riemann Sphere; 1.3. Tangent Vectors and Mappings; 1.3a. Tangent or "Contravariant" Vectors; 1.3b. Vectors as Differential Operators; 1.3c. The Tangent Space to Mn at a Point; 1.3d. Mappings and Submanifolds of Manifolds; 1.3e. Change of Coordinates; 1.4. Vector Fields and Flows; 1.4a. Vector Fields and Flows on Rn; 1.4b. Vector Fields on Manifolds; 1.4c. Straightening Flows; CHAPTER 2; Tensors and Exterior Forms; 2.1. Covectors and Riemannian Metrics; 2.1a. Linear Functionals and the Dual Space.
- 2.1b. The Differential of a Function2.1c. Scalar Products in Linear Algebra; 2.1d. Riemannian Manifolds and the Gradient Vector; 2.1e. Curves of Steepest Ascent; 2.2. The Tangent Bundle; 2.2a. The Tangent Bundle; 2.2b. The Unit Tangent Bundle; 2.3. The Cotangent Bundle and Phase Space; 2.3a. The Cotangent Bundle; 2.3b. The Pull-Back of a Covector; 2.3c. The Phase Space in Mechanics; 2.3d. The Poincar´e 1-Form; 2.4. Tensors; 2.4a. Covariant Tensors; 2.4b. Contravariant Tensors; 2.4c. Mixed Tensors; 2.4d. Transformation Properties of Tensors; 2.4e. Tensor Fields on Manifolds.
- 2.5. The Grassmann or Exterior Algebra.
- Provides a working knowledge of tools that are of great value in geometry and physics and in engineering.
Ämnesord
- Geometry, Differential.
- Geometry.
- Mathematical physics.
Genre
- Electronic books. (LCSH)
Klassifikation
- QC20.7 .D52 F73 2011 (LCC)
- 530.15/636 (DDC)
- Ucced (kssb/8 (machine generated))
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