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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
Innehållsförteckning Sammanfattning Ämnesord
Stäng  
  • 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)
530.15/636530.156 (DDC)
Ucced (kssb/8 (machine generated))
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