幾何矢量 (英文) 加布里埃爾.魏因賴希 9787519296711 【台灣高等教育出版社】

Name: 幾何矢量 (英文) 加布里 埃爾.魏因賴希 9787519296711 【台灣高等教育出版社】
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書名：幾何矢量 (英文)
ISBN：9787519296711
出版社：世界圖書出版公司
著編譯者：加布里埃爾.魏因賴希
頁數：115
所在地：中國大陸 *此為代購商品
書號：1583347
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內容簡介

矢量（vector）又被翻譯為向量。這個概念最初來自直觀的幾何矢量。在數學中，矢量的含義要比幾何矢量更廣泛，也就是說，幾何矢量雖然是數學家所研究的矢量的一種，但不是唯一的一種，廣義來說任何矢量空間中的元素都叫做矢量。本書是「芝加哥大學物理學講義」的作品之一，向讀者介紹了幾何矢量在物理學上的應用。

Preface
1: Prologue: What This Book Is About
1 1 Introduction
1 2 Where We Begin
1 3 What Vectors Are Not
1 4 What Traditional Vectors Are
1 5 Do Vectors Have a Location?
1 6 Coordinate Transformations vs Distortions of System
1 7 Why Is Topological Invariance Important?
Problems
2: Vector Types and Vector Operations
2 1 What Is the Problem?
2 2 Stacks
2 3 The Size of Mathematical Objects
2 4 Orientation of Lines and of Planes
2 5 Algebra of Arrows and of Stacks
2 6 The Dot Product
Problems
3: More Operations， More Vectors
3 1 A New Kind of Product
3 2 The Cross Product of Arrows
3 3 Polar and Axial Sense Genders
3 4 Algebra of Polar and Axial Senses
3 5 Polar and Axial Scalars
3 6 The Fourth and Last Vector: The Sheaf
3 7 Algebra of Thumbtacks and Sheaves
Problems
4: Completion of the Menagerie
4 1 Reprise: The Need for Invariance
4 2 What Is Still Missing
4 3 The Remaining Cross Products
4 4 More Dot Products: Scalar Densities and Capacities
4 5 Formalization of Nomenclature
4 6 The Geometrical Meaning of "Co-" and 「Contra
4 7 Multiplication by Scalar Densities and Capacities
Problems
5: Fields and the Geometrical Calculus
5 1 Fields
5 2 The Gradient
5 3 The Curl
5 4 The Divergence
5 5 The Inverse Operations
5 6 The Meaning of Differential Operations
Problems
6: Coordinates and Components
6 1 Coordinate Systems
6 2 The Bases of Scalar Capacities and Densities
6 3 The Arrow and Stack Bases
6 4 Stack-Arrow Dot Product in Terms of Components
6 5 How Coordinate Systems Differ
6 6 But Off the Record， How Does It Look?
Problems
7: The Grand Algebraization Rule
7 1 Statement of the Rule
7 2 The Remaining Bases
7 3 Cross Products in Terms of Components
7 4 Hermaphrodite Sense Gender of the Bases
7 5 Computation of the Gradient
7 6 Computation of the Curl
7 7 And Finally， the Divergence
Problems
8: Goodbye to the Rubber Universe
8 1 The Need for Measurement
8 2 Example: The Electromagnetic Field
8 3 Underlying Cartesian System
8 4 Legalization of Illegal Operations; the Laplacian
8 5 The "Del" Operator
8 6 Orthogonal Systems
8 7 The Metric
Problems
9: Epilogue: Where This Book Leaves Us
9 1 Some Remaining Problems
9 2 Number of Dimensions
9 3 Curved Spaces
9 4 Indefinite Metric
9 5 The Nature of Tensor Analysis
9 6 Conclusion
Index

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