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首页 赋范向量空间上的微积分(英文版)txt,chm,pdf,epub,mobi下载作者:Rodney Coleman 出版社: 世界图书出版公司 原作名: Calculus on Normed Vector Spaces 出版年: 2016-1-1 页数: 249 定价: 45.00元 装帧: 平装 ISBN: 9787519200190 内容简介 · · · · · ·本书适合高年级本科生或低年级研究生学习赋范向量空间上的微积分。书中不仅有成熟的数学模型,还有基础的微积分和线性代数。在必要处对重要拓扑学和泛函分析也作了介绍。 为了讲述赋范向量空间上的微积分在多变量函数基础微积分上的应用,该书是为数不多的几本能够连接初级文本和高级文本的教科书。书中穿插的该理论非平凡解的应用以及有趣的练习为读者学习赋范向量空间上的微积分提供了动力。目次：赋范向量空间；微分法；中值定理；高阶倒数与微分；泰勒定理及应用；Hilbert空间；凸函数；逆映射定理和隐式映射定理；向量场；向量场流；变分泛函：导论；参考文献；索引。 读者对象：数学专业高年级本科生及低年级研究生以及相关专业的科研工作者、技术人员。 作者简介 · · · · · ·Rodney Coleman（R.科尔曼,法国）是国际知名学者,在数学界享有盛誉。本书凝聚了作者多年科研和教学成果,适用于科研工作者、高校教师和研究生。 目录 · · · · · ·Preface1 Normed Vector Spaces 1.1 First Notions 1.2 Limits and Continuity 1.3 Open and Closed Sets 1.4 Compactness · · · · · ·() Preface 1 Normed Vector Spaces 1.1 First Notions 1.2 Limits and Continuity 1.3 Open and Closed Sets 1.4 Compactness 1.5 Banach Spaces 1.6 Linear and Polynomial Mappings 1.7 Normed Algebras 1.8 The Exponential Mapping Appendix： The Fundamental Theorem of Algebra 2 Differentiation 2.1 Directional Derivatives 2.2 The Differential 2.3 Differentials of Compositions 2.4 Mappings of Class C1 2.5 Extrema 2.6 Differentiability of the Norm Appendix： Gateaux Differentiability 3 Mean Value Theorems 3.1 Generalizing the Mean Value Theorem 3.2 Partial Differentials 3.3 Integration 3.4 Differentiation under the Integral Sign 4 Higher Derivatives and Differentials 4.1 Schwarz's Theorem 4.2 Operationson Ck—Mappings 4.3 Multilinear Mappings 4.4 Higher Differentials 4.5 Higher Differentials and Higher Derivatives 4.6 Cartesian Product Image Spaces 4.7 Higher Partial Differentials 4.8 Generalizing Ck to Normed Vector Spaces 4.9 Leibniz's Rule 5 Taylor Theorems and Applicahons 5.1 Taylor Formulas 5.2 Asymptotic Developments 5.3 Extrema： Second—Order Conditions Appendix： Homogeneous Polynomials 6 Hilbert Spaces 6.1 Basic Notions 6.2 Projections 6.3 The Distance Mapping 6.4 The Riesz Representation Theorem 7 Convex Functions 7.1 Preliminary Results 7.2 Continuity of Convex Functions 7.3 Differentiable Convex Functions 7.4 Extrema of Convex Functions Appendix： Convex Polyhedra 8 The Inverse and Implicit Mapping Theorems 8.1 The Inverse Mapping Theorem 8.2 The Implicit Mapping Theorem 8.3 The Rank Theorem 8.4 Constrained Extrema Appendix 1： Bijective Continuous Linear Mappings Appendix 2： Contractions 9 Vector Fields 9.1 Existence of Integral Curves 9.2 Initial Conditions 9.3 Geometrical Properties of Integral Curves 9.4 Complete Vector Fields Appendix： A Useful Result on Smooth Functions 10 The Flow of a Vector Field 10.1 Continuity of the Flow 10.2 Differentiability of the Flow 10.3 Higher Differentiability of the Flow 10.4 The Reduced Flow 10.5 One—Parameter Subgroups 11 The Calculus of Variations： An Introduction 11.1 The Space C1（I, E） 11.2 Lagrangian Mappings 11.3 Fixed Endpoint Problems 11.4 Euler—LagrangeEquations 11.5 Convexity 11.6 The Class of an Extremal References Index · · · · · · () |
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作者： 欧阳了个惠琳
比较有兴趣
生动有趣的诠释了
非常好的一本书,值得拥有。
开始看的很有意思