最 低 价：￥243.70
定 价：￥270.75
作 者：DominicG.B. Edelen 著 著
出 版 社：Oversea Publishing House
出版时间：2004-12-1
I S B N：9780486438719
| ERRATA PART ONE.VECTORS AND FORMS 1.Mathematical Preliminaries 1-1.Number Space, Points, and Coordinates 1-2.Composition of Mappings 1-3.Some Useful Theorems 1-4.Systems of Autonomous First-Order Differential Equations 1-5.Vector Spaces, Dual Spaces, and Algebras 2.Vector Fields 2-1.The Tangent to a Curve at a Point 2-2.The Tangent Space T(En) and Vector Fields on En 2-3.Operator Representations of Vector Fields, 2-4.Orbits 2-5.Linear and Quasilinear First-Order Partial Differential Equations 2-6.The Natural Lie Algebra of T(En) 2-7.Lie Subalgebra of T(En) and Systems of Linear First-Order Partial Differential Equations 2-8.Behavior under Mappings, 3.Exterior Forms 3-1.The Dual Space T*(En) 3-2.The Exterior or "Veck" Product 3-3.Algebraic Results 3-4.Inner Multiplication, 3-5.Top Down Generation of Bases 3-6.Ideals of A(En). 3-7.Behavior under Mappings, 4.Exterior Derivatives, Lie Derivatives, and Integration 4-1.The Exterior Derivative 4-2.Closed Ideals and a Confluence of Ideas. 4-3.The Frobenius Theorem 4-4.The Darboux Class of a 1-Form and the Darboux Theorem 4-5.Finite Deformations and Lie Derivatives 4-6.Ideals and Isovector Fields 4-7.Integration of Exterior Forms, Stokes' Theorem,and the Divergence Theorem 5.Antiexact Differential Forms and Homotopy Operators 5-1.Perspective 5-2.Starshaped Regions 5-3.The Homotopy Operator H, 5-4.The Exact Part of a Form and the Vector Subspace of Exact Forms 5-5.The Module of Antiexact Forms 5-6.Representations 5-7.Change of Center 5-8.Behavior under Mappings 5-9.An Introductory Problem 5-10.Representations for 2-Forms That Are Not Closed 5-11.Differential Systems of Degree k and Class r 5-12.Integration of the Connection Equations 5-13.The Attitude Matrix of a Differential System 5-14.Integration of the Curvature Equations …… PART TWO. APPLICATIONS TO MATHEMATICS 6.Isovector Methods for Second-Order Partial Differential Equations 7.Calculus of Variations PART THREE. APPLICATIONS TO PHYSICS 8.Modern Thermodynamics 9.Electrodynamics with Electric and Magnetic charges 10.Gauge Theories Appendix Addendum 1 Addendum 2 Index |
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