向量微积分、线性代数和微分形式 第3版
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作者(美)哈伯德 著
出版社世界图书出版公司
ISBN9787510061509
出版时间2013-10
版次1
装帧平装
开本16开
纸张胶版纸
页数802页
定价169元
上书时间2024-02-24
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基本信息
书名:向量微积分、线性代数和微分形式 第3版
定价：169.00元
作者:(美)哈伯德 著
出版社：世界图书出版公司
出版日期：2013-10-01
ISBN：9787510061509
字数：
页码：802
版次：1
装帧：平装
开本：16开
商品重量：
编辑推荐
《向量微积分、线性代数和微分形式(第3版)》是一部优秀的微积分教材，好评不断。引用上评论“是一本必选教材。”“是微积分教学方法的一次革新。”
内容提要
《向量微积分、线性代数和微分形式(第3版)》是一部优秀的微积分教材，好评不断。引用上评论“是一本必选教材。”“是微积分教学方法的一次革新。”本书材料的选择和编排有不同于标准方法的三点：(一)在这个水平的研究中，线性代数是研究多变量微积分的极其方便的环境和语言，非线性更像是一个衍生产品；(二)强调计算有效算法，并且通过这些算术工作来证明定理；(三)运用微分形式推广更高维的积分定理。 目次：预备知识；向量、矩阵和导数；解方程；流形、泰勒多项式和二次型、曲率；积分；流形的体积；形式和向量微积分。附录：分析。 读者对象：数学专业的本科生以及想学习微积分知识的广大非专业专业人士。
目录
prefacechapter 0 preliminaries0.0 introductio0.1 reading mathematics0.2 quantifiers and negatio0.3 set theory0.4 functions0.5 real numbers0.6 infinite sets0.7 complex numberschapter 1 vectors~ matrices, and derivatives1.0 introductio1.1 introducing the actors: points and vectors1.2 introducing the actors: matrices1.3 matrix multiplication as a linear transformatio1.4 the geometry of r1.5 limits and continuity1.6 four big theorems1.7 derivatives in several variables as lineartransformations1.8 rules for computing derivatives1.9 the mean value theorem and criteria for differentiability1.10 review exercises for chapter 1chapter 2 solving equations2.0 introductio2.1 the main algorithm: row reductio2.2 solving equations with row reductio2.3 matrix inverses and elementary matrices2.4 linear combinations, span, and linear independence2.5 kernels, images, and the dimension formula2.6 abstract vector spaces2.7 eigenvectors and eigenvalues2.8 newton's method2.9 superconvergence2.10 the inverse and implicit function theorems2.11 review exercises for chapter 2chapter 3 manifolds, taylor polynomials, quadratic forms, andcurvature3.0 introductio3.1 manifolds3.2 tangent spaces3.3 taylor polynomials in several variables3.4 rules for computing taylor polynomials3.5 quadratic forms3.6 classifying critical points of fimctions3.7 constrained critical points and lagrange multipliers3.8 geometry of curves and surfaces3.9 review exercises for chapter 3chapter 4 integratio4.0 introductio4.1 defining the integral4.2 probability and centers of gravity4.3 what functions can be integrated?4.4 measure zero4.5 fhbini's theorem and iterated integrals4.6 numerical methods of integratio4.7 other pavings4.8 determinants4.9 volumes and determinants4.10 the change of variables formula4.11 lebesgue integrals4.12 review exercises for chapter 4chapter 5 volumes of manifolds5.0 introductio5.1 parallelograms and their volumes5.2 parametrizations5.3 computing volumes of manifolds5.4 integration and curvature5.5 fractals and fractional dimensio5.6 review exercises for chapter 5chapter 6 forms and vector calculus6.0 introductio6.1 forms on r6.2 integrating form fields over parametrized domains6.3 orientation of manifolds6.4 integrating forms over oriented manifolds6.5 forms in the language of vector calculus6.6 boundary orientatio6.7 the exterior derivative6.8 grad, curl, div, and all that6.9 electromagnetism6.10 the generalized stokes's theorem6.11 the integral theorems of vector calculus6.12 potentials6.13 review exercises for chapter 6appendix: analysisA.0 introductioA.1 arithmetic of real numbersA.2 cubic and quartic equationsA.3 two results in topology: nested compact sets andheine-borelA.4 proof of the chain ruleA.5 proof of kantorovich's theoremA.6 proof of lemma 2.9.5 (superconvergence)A.7 proof of differentiability of the inverse functioA.8 proof of the implicit function theoremA.9 proving equality of crossed partialsA.10 functions with many vanishing partial derivativesA.11 proving rules for taylor polynomials; big o and little oA.12 taylor's theorem with remainderA.13 proving theorem 3.5.3 (completing squares)A.14 geometry of curves and surfaces: proofsA.15 stirling's formula and proof of the central limittheoremA.16 proving fubiul's theoremA.17 justifying the use of other pavingsA.18 results concerning the determinantA.19 change of variables formula: a rigorous proofA.20 justifying volume 0A.21 lebesgue measure and proofs for lebesgue integralsA.22 justifying the change of parametrizatioA.23 computing the exterior derivativeA.24 the pullbackA.25 proving stokes's theorembibliographyphoto creditsindex
作者介绍
作者：（美国）哈伯德（John H.Hubbard） （美国）Barbara Burke Hubbard
序言
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