具体描述
基本信息
书名:单变量微积分
定价：80.00元
售价：60.0元,便宜20.0元,折扣75
作者:邹云志
出版社：世界图书出版公司
出版日期：2015-05-01
ISBN：9787510094903
字数：
页码：350
版次：1
装帧：平装
开本：16开
商品重量：0.4kg
编辑推荐
内容提要
Irecently years, more and more Chinese students are going overseas, either as exchange students, or to pursue degrees. At the same time, more and more students are ing from other countries to Chinese universities to further their studies. We've noticed that iterms of both knowledge transfer and intercultural munication, the English language has played aindispensable role. Furthermore, it is the interest of these students to have a smooth transitiofrom one system to another, for their credits to transfer, and for them to immerse themselves ithe new environment as quickly as possible. To this end, more and more Chinese schools are offering courses delivered bilingually or iEnglish to enhance students' international outlook.
One of the greatest challenges ioffering Chinese students a course iEnglish is finding a suitable textbook: the textbook must seriously consider what students have done itheir high schools; it must meet the national and local official course standards; and it should resonate with significant international flavors so as to benefit students.
目录
CHAPTER 1 Prereqrusites for Calculus
1.1 Overview ofCalculus
1.2 Sets and Numbers
1.2.1 Sets
1.2.2 Numbers
1.2.3 The Least Upper Bound Property
1.2.4 The Extended Real Number System
1.2.5 1ntervals
1.3 Functions
1.3.1 Definitioofa Function
1.3.2 Graph ofa Function
1.3.3 Some Basic Functions and Their Graphs
1.3.4 Building New Functions
1.3.5 Fundamental Elementary Functions
1.3.6 Properties ofFunctions
1.4 Exercises
CHAPTER 2 Limits and Continruty
2.1 Rates ofChange and Derivatives
2.2 Limits of a Function
2.2.1 Definitioof a Limit
2.2.2 Properties of Limits of Functions
2.2.3 Limit Laws
2.2.4 One-sided Liruits
2.2.5 Limits Involving Infinity and Asymptotes
2.3 Limits of Sequences
2.3.1 Definitions and Properties
2.3.2 Subsequences
2.4 Squeeze Theorem and Cauchy's Theorem
2.5 Infinitesimal Functions and Asymptotic Functions
2.6 Continuous and Discontinuous Functions
2.6.1 Continuity and Discontinuity
2.6.2 Continuous Functions
2.6.3 Theorems oContinuous Functions
2.6.4 Uniform Continuity
2.7 Some Proofs iChapter
2.8 Exercises
CHAPTER 3 I'he Derivative
3.1 Derivative ofa Functioat a Point
3.1.1 Instantaneous Rates of Change and Derivatives Revisited
3.1.2 One-sided Derivatives
3.1.3 A FunctioMay Fail to Have a Derivative at a Point
3.2 Derivative as a Function
3.2.1 Graphing the Derivative of a Function
3.2.2 Derivatives of Some Basic Functions
3 .3 Derivative Laws
3.4 Derivative of aJnverse Function
3.5 Differentiating a Composite Functio- The ChaiRule
3.6 Derivatives ofHigher Orders
3.7 Implicit Differentiation
3.8 Functions Defined by Parametric and Polar Equations
3.8.1 Functions Defined by Parametric Equations
3.8.2 Polar Curves
3.9 Related Rates ofChange
3.10 The Tangent Line Approximatioand the Differentia
3.10.1 Linearization
3.10.2 Differentials
3.11 Derivative Rules-Summary
3.12 Exercises
CHAPTER 4 Applications of the Derivative
4.1 Extreme Values and The Candidate Theorem
4.2 The MeaValue Theore
4.3 Monotonic Functions and The First Derivative Test
4.3.1 Monotonic Functions
4.3.2 The First Derivative Test
4.4 Extended MeaValue Theorem and the L'Hopital's Rules
4.4.1 Extended MeaValue Theorem
……
CHAPTER 5 The Definite Integral
CHAPTER 6 Techniques for Integratioand Improper Integrals
CHAPTER 7 Applications of the Definite Integral
CHAPTER 8 Infinite Series, Sequences, and Approximations
作者介绍
文摘
序言
CHAPTER 1 Prereqrusites for Calculus
1.1 Overview ofCalculus
1.2 Sets and Numbers
1.2.1 Sets
1.2.2 Numbers
1.2.3 The Least Upper Bound Property
1.2.4 The Extended Real Number System
1.2.5 1ntervals
1.3 Functions
1.3.1 Definitioofa Function
1.3.2 Graph ofa Function
1.3.3 Some Basic Functions and Their Graphs
1.3.4 Building New Functions
1.3.5 Fundamental Elementary Functions
1.3.6 Properties ofFunctions
1.4 Exercises
CHAPTER 2 Limits and Continruty
2.1 Rates ofChange and Derivatives
2.2 Limits of a Function
2.2.1 Definitioof a Limit
2.2.2 Properties of Limits of Functions
2.2.3 Limit Laws
2.2.4 One-sided Liruits
2.2.5 Limits Involving Infinity and Asymptotes
2.3 Limits of Sequences
2.3.1 Definitions and Properties
2.3.2 Subsequences
2.4 Squeeze Theorem and Cauchy's Theorem
2.5 Infinitesimal Functions and Asymptotic Functions
2.6 Continuous and Discontinuous Functions
2.6.1 Continuity and Discontinuity
2.6.2 Continuous Functions
2.6.3 Theorems oContinuous Functions
2.6.4 Uniform Continuity
2.7 Some Proofs iChapter
2.8 Exercises
CHAPTER 3 I'he Derivative
3.1 Derivative ofa Functioat a Point
3.1.1 Instantaneous Rates of Change and Derivatives Revisited
3.1.2 One-sided Derivatives
3.1.3 A FunctioMay Fail to Have a Derivative at a Point
3.2 Derivative as a Function
3.2.1 Graphing the Derivative of a Function
3.2.2 Derivatives of Some Basic Functions
3 .3 Derivative Laws
3.4 Derivative of aJnverse Function
3.5 Differentiating a Composite Functio- The ChaiRule
3.6 Derivatives ofHigher Orders
3.7 Implicit Differentiation
3.8 Functions Defined by Parametric and Polar Equations
3.8.1 Functions Defined by Parametric Equations
3.8.2 Polar Curves
3.9 Related Rates ofChange
3.10 The Tangent Line Approximatioand the Differentia
3.10.1 Linearization
3.10.2 Differentials
3.11 Derivative Rules-Summary
3.12 Exercises
CHAPTER 4 Applications of the Derivative
4.1 Extreme Values and The Candidate Theorem
4.2 The MeaValue Theore
4.3 Monotonic Functions and The First Derivative Test
4.3.1 Monotonic Functions
4.3.2 The First Derivative Test
4.4 Extended MeaValue Theorem and the L'Hopital's Rules
4.4.1 Extended MeaValue Theorem
……
CHAPTER 5 The Definite Integral
CHAPTER 6 Techniques for Integratioand Improper Integrals
CHAPTER 7 Applications of the Definite Integral
CHAPTER 8 Infinite Series, Sequences, and Approximations
用户评价
这本书的装帧设计简直是艺术品，那种沉甸甸的质感，封面选用的哑光纸张，触摸起来细腻又高级，让人爱不释手。内页的排版也看得出是用心了，字体选择的衬线体，阅读起来非常舒适，长篇的公式推导也不会让人感到视觉疲劳。不过，我得说，第一遍翻阅时，我几乎被那些密密麻麻的符号阵仗给‘震慑’住了。它不像我以前看过的那些入门教材那样，上来就用大量的日常例子来‘软化’读者。这本书是直接亮剑，毫不客气地把最核心、最抽象的概念就摆在你面前。比如，介绍极限的时候，那种严谨的$epsilon-delta$定义，读起来简直像在啃一块坚硬的花岗岩，需要反复咀嚼才能体会到其中蕴含的数学美感。我花了很长时间才适应这种‘高冷’的叙事风格，但一旦跨过那道门槛，你会发现，这种开门见山的直击本质，反而建立了一种极其扎实的数学直觉。它不屑于用太多拐弯抹角的比喻，而是用最精炼的语言，构建起一个逻辑自洽的体系。对于那些追求深度和纯粹性的读者来说，这无疑是一本宝藏，但对于初学者，可能需要一个非常耐心的引导者陪伴。
评分我必须承认，这本书在定理的证明环节展现出的深度和广度，远超我预期的任何一本微积分教材。它没有将证明过程‘降维打击’成几个简单的步骤，而是将每一步逻辑的跳跃都进行了详尽的、近乎于‘吹毛求疵’的论证。特别是关于反导数的存在性以及中值定理的推导部分，作者似乎特意花了大量的篇幅去探讨那些在普通教材中常常被‘一笔带过’的边界情况和特殊条件。我记得有一个关于泰勒级数余项表达式的讨论，它详细对比了四种不同余项形式的适用场景和收敛速度的差异，这简直是为那些准备考研或者打算深入研究数学分析的同学量身定做的‘秘籍’。我甚至怀疑作者是不是偷偷地在向更高阶的分析学课程‘输送’知识点。唯一让我感到略微头疼的是，一些高级的证明过程需要读者对集合论和拓扑学的基础概念有非常清晰的认识，否则，当你看到诸如‘紧致集’或者‘完备性’这类词汇在证明中自然出现时，会有一种掉队的感觉。它要求你不仅要知道‘怎么做’，更要知道‘为什么能这么做’。
评分从教学法革新的角度来看，这本书的叙事结构非常独特，它似乎颠覆了传统的‘定义-定理-例题’的线性流程。作者更倾向于以‘问题驱动’的方式展开章节内容。比如，在讲解定积分与不定积分的关系时，它不是先给出微积分基本定理，而是先提出一个‘如何计算不规则形状的面积’的古老难题，然后层层剥笋地引入黎曼和、上积分、下积分的概念，最终才水到渠成地引出那个伟大的定理。这种‘历史重演’式的教学方法，虽然在初次阅读时会显得有点慢热，但它极大地增强了知识的‘源头活水’感，让你真切地感受到数学是如何一步步发展和完善起来的。这种叙事策略，让那些原本可能枯燥的理论推导，瞬间充满了历史的厚重感和探索的激动。它培养的不是一个公式的搬运工，而是一个数学思想的追随者。
评分这本书的‘跨界’参考价值也是一个亮点，它在某些章节的讨论中，会不自觉地引入一些其他学科的术语和概念，使得读者能够跳出纯数学的象牙塔，看到微积分在现实世界中的巨大影响力。例如，在涉及级数收敛性的讨论中，作者巧妙地引用了物理学中关于量子态叠加的某些思想来辅助理解，虽然没有深入展开，但这种‘点到为止’的暗示，极大地激发了我的好奇心，促使我主动去查阅相关的交叉学科资料。在我看来，一本好的教材，不应该只是一门学科的圣经，更应该是一座桥梁，连接着不同的知识领域。这本书在这方面做得非常出色，它让你在学习如何求导、如何积分的同时，也在潜移默化地拓宽你的知识边界。它就像一个经验丰富的老者，在教你基础技艺的同时，不断向你描绘更广阔的江湖风光，让人心驰神往，迫不及待想去探索。
评分这本书的习题设计是其精髓，也是我个人感觉最‘折磨人’但也最有收获的部分。它没有采用那种‘一题多变’的重复训练模式，而是更侧重于‘一题多解’和‘概念应用深度’的考察。我做完第三章后面那些关于曲线曲率和弧长计算的题目后，感觉自己对空间想象力的要求达到了一个新的高度。很多题目都不是直接套用公式就能解决的，它要求你必须先在脑海中构建一个清晰的物理模型或者几何场景，然后将微积分工具恰当地‘嵌入’进去。更妙的是，在书的末尾，它附带了一个非常精简的‘解题思路提示’部分，但这个提示往往只给出一个方向性的引导，而不是具体的步骤，这极大地锻炼了我们独立解决问题的能力。我有一个习惯，就是把那些花了我超过一小时才解出来的题目，标记出来，然后过一段时间再重新做一遍，每一次重做，似乎都能发现新的角度和更优雅的解法。这套习题集，是真正意义上的‘试金石’。
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