数学物理的几何方法
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作者（英）舒茨 著
出版社世界图书出版公司
ISBN9787510004513
出版时间2009-06
版次1
装帧平装
开本16开
纸张胶版纸
页数250页
定价35元
上书时间2024-07-31
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基本信息
书名:数学物理的几何方法
定价：35元
作者:（英）舒茨 著
出版社：世界图书出版公司
出版日期：2009-06-01
ISBN：9787510004513
字数：
页码：250
版次：1
装帧：平装
开本：24开
商品重量：
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内容提要
目录
1 Some basic mathematics 1.1 The space Rn and its topology 1.2 Mappings 1.3 Real analysis 1.4 Group theory 1.5 Linear algebra 1.6 The algebra of square matrices 1.7 Bibliography2 Dffferentiable manifolds and tensors 2.1 Def'mition of a manifold 2.2 The sphere as a manifold 2.3 Other examples of manifolds 2.4 Global considerations 2.5 Curves 2.6 Functions on M 2.7 Vectors and vector fields 2.8 Basis vectors and basis vector fields 2.9 Fiber bundles 2.10 Examples of fiber bundles 2.11 A deeper look at fiber bundles 2.12 Vector fields and integral curves 2.13 Exponentiation of the operator d/dZ 2.14 Lie brackets and noncoordinate bases 2.15 When is a basis a coordinate basis？ 2.16 One-forms 2.17 Examples of one-forms 2.18 The Dirac delta function 2.19 The gradient and the pictorial representation of a one-form 2.20 Basis one-forms and components of one-forms 2.21 Index notation 2.22 Tensors and tensor fields 2.23 Examples of tensors 2.24 Components of tensors and the outer product 2.25 Contraction 2.26 Basis transformations 2.27 Tensor operations on components 2.28 Functions and scalars 2.29 The metric tensor on a vector space 2.30 The metric tensor field on a manifold 2.31 Special relativity 2.32 Bibliography3 Lie derivatives and Lie groups 3.1 Introduction: how a vector field maps a manifold into itself 3.2 Lie dragging a function 3.3 Lie dragging a vector field 3.4 Lie derivatives 3.5 Lie derivative of a one-form 3.6 Submanifolds 3.7 Frobenius' theorem (vector field version) 3.8 Proof of Frobenius' theorem 3.9 An example: the generators ors2 3.10 Invariance 3.11 Killing vector fields 3.12 Killing vectors and conserved quantities in particle dynamics 3.13 Axial symmetry 3.14 Abstract Lie groups 3.15 Examples of Lie groups 3.16 Lie algebras and their groups 3.17 Realizations and representatidns 3.18 Spherical symmetry, spherical harmonics and representations of the rotation group 3.19 Bibliography4 Differential forms A The algebra and integral calculus of forms 4.1 Definition of volume - the geometrical role of differential forms 4.2 Notation and definitions for antisymmetric tensors 4.3 Differential forms 4.4 Manipulating differential forms 4.5 Restriction of forms 4.6 Fields of forms5 Applications in physics A Thermodynamics6 Connections for Riemannian manifolds and gauge theoriesAppendix: solutions and hints for selected exercisesNotationIndex
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