数学物理的几何方法(英文版)(Geometrical Methods of Mathematical Physics) 7510004519/978751000

《数学物理的几何方法(英文版)》讲述了：This book alms to introduce the beginning or working physicist to awide range of aualytic tools which have their or/gin in differential geometry andwhich have recently found increasing use in theoretical physics. It is not uncom-mon today for a physicist's mathematical education to ignore all but the sim-plest geometrical ideas, despite the fact that young physicists are encouraged todevelop mental 'pictures' and 'intuition' appropriate to physical phenomena.This curious neglect of 'pictures' of one's mathematical tools may be seen as the outcome of a gradual evolution over many centuries. Geometry was certainly extremely important to ancient and medieval natural philosophers; it was ingeometrical terms that Ptolemy, Copernicus, Kepler, and Galileo all expressedtheir thinking. But when Descartes introduced coordinates into Euclideangeometry, he showed that the study of geometry could be regarded as an appli.cation of algrebra. Since then, the/mportance of the study of geometry in theeducation of scientists has steadily 《数学物理的几何方法(英文版)》是由世界图书出版公司出版的。 作者：(英国)舒茨(Schutz.B.) 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 Bibliography 2 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 Bibliography 3 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 In

ISBN	7510004519/978751000
出版社	世界图书出版公司
尺寸	24