- 物理几何学导论(第3版)(英文版)
- - 作者：(美)T.弗兰克尔|责编:刘慧//高蓉
  - 出版社：世界图书出版公司
  - ISBN：9787519214715
  - 出版日期：2016/07/01
  - 页数：686
- 售价：63.6

内容大纲
本书主要介绍关于外微分形式，微分几何，代数微分拓扑，李群，向量丛，等方面的部分内容，这些内容也是理解经典现代物理和工程的基本前提。本书也呈现了几何概念及其在工程方面的应用。本书也可用于自学。读者对象：物理，工程和数学专业的研究生。
作者介绍
目录
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
  0.b.Two Kinds of Vectors
  0.c.Superscripts,Subscripts,Summation Convention
  0.d.Riemannian Metrics
  0.e.Tensors
  Integrals and Exterior Forms
  0.f.Line Integrals
  0.g.Exterior 2-Forms
  0.h.Exterior p-Forms and Algebra in Rn
  0.i.The Exterior Differential d
  0.j.The Push-Forward of a Vector and the Pull-Back of a Form
  o.k.Surface Integrals and“Stokes'Theorem”
  0.1.Electromagnetism,or,Is it a Vector or a Form?
  C.m.Interior Products
  o.n.Volume Forms and Cartan's Vector Valued Exterior Forms
  0.o.Magnetic Field for Curent in a Straight Wire
  Elasticity and Stresses
  0.p.Cauchy Stress,Floating Bodies,Twisted Cylinders,and Strain Energy
  0.q.Sketch of Cauchy's“First Theorem”
  0.r.Sketch of Cauchy's“Second Theorem,”Moments as Generators of Rotations
  0.s. ARemarkable Formula for Differentiating Line,Surface. and...,Integrals
Ⅰ  Manifolds,Tensors,and Exterior Forms
  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 Manifold
      1.2d.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

  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 Function
      2.1c.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 Poincare 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
  ……
Ⅱ  Geometry and Topology
Ⅲ  Lie Groups, Bundles, and Chern Forms
References
Index

内容大纲

作者介绍

目录

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