Vector analysis矢量分析
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作者： Klaus Janich， Leslie D. Kay著
出 版 社：
出版时间： 2001-2-1字数：版次： 1页数： 281印刷时间： 2001/02/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387986494包装： 精装内容简介
The present book is a marvelous introduction in the modern theory of manifolds and differential forms. The undergraduate student can closely examine tangent spaces, basic concepts of differential forms, integration on manifolds, Stokes theorem, de Rham- cohomology theorem, differential forms on Riema-nnian manifolds, elements of the theory of differential equations on manifolds (Laplace-Beltrami operators). Every chapter contains useful exercises for the students.¿ ¿ ZENTRALBLATT MATH
目录
Preface to the English Edition
Preface to the First German Edition
1Differentiable Manifolds
1.1 The Concept of a Manifold
1.2 Differentiable Maps
1.3 The Rank
1.4 Submanifolds
1.5 Examples of Manifolds
1.6 Sums, Products, and Quotients of Manifolds
1.7 Will Submanifolds of Euclidean Spaces Do?
1.8 Test
1.9 Exercises
1.10 Hints for the Exercises
2The Tangent Space
2.1 Tangent Spaces in Euclidean Space
2.2 Three Versions of the Concept of a Tangent Space
2.3 Equivalence of the Three Versions
2.4 Definition of the Tangent Space
2.5 The Differential
2.6 The Tangent Spaces to a Vector Space
2.7 Velocity Vectors of Curves
2.8 Another Look at the Ricci Calculus
2.9 Test
2.10 Exercises
2.11 Hints for the Exercises
3Differential Forms
3.1 Alternating k-Forms
3.2 The Components of an Alternating k-Form
3.3 Alternating n-Forms and the Determinant
3.4 Differential Forms
3.5 One-Forms
3.6 Test
3.7 Exercises
3.8 Hints for the Exercises
4The Concept of Orientation
4.1 Introduction
4.2 The TWO Orientations of an n-Dimensional Real Vector Space
4.3 Oriented Manifolds
4.4 Construction of Orientations
4.5 Test
4.6 Exercises
4.7 Hints for the Exercises
5Integration on Manifolds
5.1 What Are the Right Integrands?
5.2 The Idea behind the Integration Process
5.3 Lebesgue Background Package
5.4 Definition of Integration on Manifolds
5.5 Some Properties of the Integral
5.6 Test
……
6Manifolds-with-Boundary
7 The Intuitoive Meaning of Stokes's Theorem
8 The Wedge Product and the Defintion of the Cartan Derivative
9 Stokes's Theorem
10 Classical Vector Analysis
11 De Rham Cohomology
12 Differential Forms on Riemannian Manifolds
13 Calculations in coordiates
14 Answers to the Test Questions
Bibligraphy
Index
