Single Variable Calculus: Early Transcendentals (International Metric Edition) 英文原版 [精装] pdf epub mobi txt 电子书 下载 2025

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☆☆☆☆☆

James Stewart 著

图书标签:

• 微积分
• 单变量微积分
• 高等数学
• 国际版
• 英文原版
• 精装
• 数学
• 理工科
• 大学教材
• 微积分教材

出版社： Cengage Learning

ISBN：9780538498883

版次：7

商品编码：19172452

包装：精装

出版时间：2011-01-01

页数：936

正文语种：英文

商品尺寸：26.2x22.3x3.4cm;1.789kg

内容简介

James Stewart's CALCULUS: EARLY TRANSCENDENTALS texts are widely renowned for their mathematical precision and accuracy, clarity of exposition, and outstanding examples and problem sets. Millions of students worldwide have explored calculus through Stewart's trademark style, while instructors have turned to his approach time and time again. In the Seventh Edition of SINGLE VARIABLE CALCULUS: EARLY TRANSCENDENTALS, Stewart continues to set the standard for the course while adding carefully revised content. The patient explanations, superb exercises, focus on problem solving, and carefully graded problem sets that have made Stewart's texts best-sellers continue to provide a strong foundation for the Seventh Edition. From the most unprepared student to the most mathematically gifted, Stewart's writing and presentation serve to enhance understanding and build confidence.
CourseSmart goes beyond traditional expectations–providing instant, online access to the textbooks and course materials you need and at a lower cost to your students. To request an electronic sample of this Cengage Learning title, go to: www.coursesmart.com/instructors.

目录

Diagnostic Tests.
A Preview of Calculus.
1. FUNCTIONS AND MODELS.
Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Graphing Calculators and Computers. Exponential Functions. Inverse Functions and Logarithms. Review. Principles of Problem Solving.

2. LIMITS AND DERIVATIVES.
The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Limits at Infinity; Horizontal Asymptotes. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. Review. Problems Plus.

3. DIFFERENTIATION RULES.
Derivatives of Polynomials and Exponential Functions. Applied Project: Building a Better Roller Coaster. The Product and Quotient Rules. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Derivatives of Logarithmic Functions. Rates of Change in the Natural and Social Sciences. Exponential Growth and Decay. Related Rates. Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials. Hyperbolic Functions. Review. Problems Plus.

4. APPLICATIONS OF DIFFERENTIATION.
Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. The Mean Value Theorem. How Derivatives Affect the Shape of a Graph. Indeterminate Forms and L'Hospital's Rule. Writing Project: The Origins of l'Hospital's Rule. Summary of Curve Sketching. Graphing with Calculus and Calculators. Optimization Problems. Applied Project: The Shape of a Can. Newton's Method. Antiderivatives. Review. Problems Plus.

5. INTEGRALS.
Areas and Distances. The Definite Integral. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change Theorem. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule. Review. Problems Plus.

6. APPLICATIONS OF INTEGRATION.
Areas between Curves. Volume. Volumes by Cylindrical Shells. Work. Average Value of a Function. Applied Project: Where to Sit at the Movies. Review. Problems Plus.

7. TECHNIQUES OF INTEGRATION.
Integration by Parts. Trigonometric Integrals. Trigonometric Substitution. Integration of Rational Functions by Partial Fractions. Strategy for Integration. Integration Using Tables and Computer Algebra Systems. Discovery Project: Patterns in Integrals. Approximate Integration. Improper Integrals. Review. Problems Plus.

8. FURTHER APPLICATIONS OF INTEGRATION.
Arc Length. Discovery Project: Arc Length Contest. Area of a Surface of Revolution. Discovery Project: Rotating on a Slant. Applications to Physics and Engineering. Discovery Project: Complementary Coffee Cups. Applications to Economics and Biology. Probability. Review. Problems Plus.

9. DIFFERENTIAL EQUATIONS.
Modeling with Differential Equations. Direction Fields and Euler's Method. Separable Equations. Applied Project: Which is Faster, Going Up or Coming Down? Models for Population Growth. Applied Project: Calculus and Baseball. Linear Equations. Predator-Prey Systems. Review. Problems Plus.

10. PARAMETRIC EQUATIONS AND POLAR COORDINATES.
Curves Defined by Parametric Equations. Laboratory Project: Families of Hypocycloids. Calculus with Parametric Curves. Laboratory Project: Bezier Curves. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections. Conic Sections in Polar Coordinates. Review. Problems Plus.

11. INFINITE SEQUENCES AND SERIES.
Sequences. Laboratory Project: Logistic Sequences. Series. The Integral Test and Estimates of Sums. The Comparison Tests. Alternating Series. Absolute Convergence and the Ratio and Root Tests. Strategy for Testing Series. Power Series. Representations of Functions as Power Series. Taylor and Maclaurin Series. Laboratory Project: An Elusive Limit. Writing Project: How Newton Discovered the . Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars. Review. Problems Plus.

APPENDIXES.
A. Numbers, Inequalities, and Absolute Values.
B. Coordinate Geometry and Lines.
C. Graphs of Second-Degree Equations.
D. Trigonometry.
E. Sigma Notation.
F. Proofs of Theorems.
G. The Logarithm Defined as an Integral.
H. Complex Numbers.
I. Answers to Odd-Numbered Exercises.

精彩书摘

Diagnostic Tests. A Preview of Calculus. 1. FUNCTIONS AND MODELS. Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Graphing Calculators and Computers. Exponential Functions. Inverse Functions and Logarithms. Review. Principles of Problem Solving. 2. LIMITS AND DERIVATIVES. The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Limits at Infinity; Horizontal Asymptotes. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. Review. Problems Plus. 3. DIFFERENTIATION RULES. Derivatives of Polynomials and Exponential Functions. Applied Project: Building a Better Roller Coaster. The Product and Quotient Rules. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Derivatives of Logarithmic Functions. Rates of Change in the Natural and Social Sciences. Exponential Growth and Decay. Related Rates. Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials. Hyperbolic Functions. Review. Problems Plus. 4. APPLICATIONS OF DIFFERENTIATION. Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. The Mean Value Theorem. How Derivatives Affect the Shape of a Graph. Indeterminate Forms and L'Hospital's Rule. Writing Project: The Origins of l'Hospital's Rule. Summary of Curve Sketching. Graphing with Calculus and Calculators. Optimization Problems. Applied Project: The Shape of a Can. Newton's Method. Antiderivatives. Review. Problems Plus. 5. INTEGRALS. Areas and Distances. The Definite Integral. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change Theorem. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule. Review. Problems Plus. 6. APPLICATIONS OF INTEGRATION. Areas between Curves. Volume. Volumes by Cylindrical Shells. Work. Average Value of a Function. Applied Project: Where to Sit at the Movies. Review. Problems Plus. 7. TECHNIQUES OF INTEGRATION. Integration by Parts. Trigonometric Integrals. Trigonometric Substitution. Integration of Rational Functions by Partial Fractions. Strategy for Integration. Integration Using Tables and Computer Algebra Systems. Discovery Project: Patterns in Integrals. Approximate Integration. Improper Integrals. Review. Problems Plus. 8. FURTHER APPLICATIONS OF INTEGRATION. Arc Length. Discovery Project: Arc Length Contest. Area of a Surface of Revolution. Discovery Project: Rotating on a Slant. Applications to Physics and Engineering. Discovery Project: Complementary Coffee Cups. Applications to Economics and Biology. Probability. Review. Problems Plus. 9. DIFFERENTIAL EQUATIONS. Modeling with Differential Equations. Direction Fields and Euler's Method. Separable Equations. Applied Project: Which is Faster, Going Up or Coming Down? Models for Population Growth. Applied Project: Calculus and Baseball. Linear Equations. Predator-Prey Systems. Review. Problems Plus. 10. PARAMETRIC EQUATIONS AND POLAR COORDINATES. Curves Defined by Parametric Equations. Laboratory Project: Families of Hypocycloids. Calculus with Parametric Curves. Laboratory Project: Bezier Curves. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections. Conic Sections in Polar Coordinates. Review. Problems Plus. 11. INFINITE SEQUENCES AND SERIES. Sequences. Laboratory Project: Logistic Sequences. Series. The Integral Test and Estimates of Sums. The Comparison Tests. Alternating Series. Absolute Convergence and the Ratio and Root Tests. Strategy for Testing Series. Power Series. Representations of Functions as Power Series. Taylor and Maclaurin Series. Laboratory Project: An Elusive Limit. Writing Project: How Newton Discovered the . Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars. Review. Problems Plus. APPENDIXES. A. Numbers, Inequalities, and Absolute Values. B. Coordinate Geometry and Lines. C. Graphs of Second-Degree Equations. D. Trigonometry. E. Sigma Notation. F. Proofs of Theorems. G. The Logarithm Defined as an Integral. H. Complex Numbers. I. Answers to Odd-Numbered Exercises.,

前言/序言

深入微积分的基石：探索极限、导数与积分的奥秘 《多变量微积分导论：早期超越函数（国际公制版）》 是一本专为全球数学、工程学和科学领域的学生精心打造的权威教材。它以严谨的逻辑结构、清晰的教学方法，引导读者系统地掌握多变量微积分的核心概念、技术和应用。本书建立在坚实的单变量微积分基础之上，将微积分的强大工具扩展到三维及更高维度的空间，为理解复杂系统的建模和分析奠定了不可或缺的理论框架。 本书的核心目标是培养学生对空间几何直觉的深刻理解，并熟练运用向量运算、偏导数、多重积分以及向量场理论来解决实际问题。全书内容编排匠心独运，力求在概念的深度与计算的实用性之间取得完美的平衡。 第一部分：向量与空间几何的基石 教材伊始，我们首先将焦点从二维平面扩展到三维空间。向量代数是理解多变量微积分的语言。本部分详尽阐述了三维笛卡尔坐标系、向量的表示法、加法、标量乘法以及至关重要的点积（内积） 和叉积（外积）。通过对点积与角度、投影关系的深入探讨，读者能够直观地理解向量在物理学和几何学中的作用。叉积则被系统地引入，用于计算平行四边形或三角形的面积，并确定垂直于平面的法向量——这是后续曲面分析的基础。 随后，章节转向空间曲线和曲面的描述。参数方程在描述三维运动轨迹方面的优势被充分挖掘。我们详细分析了曲线的切线向量、法向量、曲率等几何量。对于曲面的研究，我们引入了二次曲面（如球面、椭球面、抛物面、双曲面等）的分类和标准方程，使读者能够熟练地在几何直觉和代数表示之间进行转换。 第二部分：偏导数的威力与梯度场 当函数依赖于多个变量时，我们如何衡量其变化率？偏导数应运而生。本部分是多变量微积分的第一个关键飞跃。我们定义了偏导数，并探讨了它们如何描述函数沿着特定方向的变化。 对偏导数的深入理解自然引向可微性的概念，并在此基础上推导出至关重要的链式法则（Chain Rule）在多变量环境下的扩展形式。通过大量的实例，读者将掌握如何处理复合函数链条中的复杂依赖关系。 梯度（Gradient）是衡量函数最大增长率和方向的矢量工具。本书详细解释了梯度向量场的性质，以及它与等值面（Level Surfaces）的垂直关系。接着，我们引入了方向导数（Directional Derivative），它将偏导数的概念推广到任意指定方向，是连接几何与分析的桥梁。 本部分的高潮在于极值理论。通过应用偏导数，我们学习如何寻找多元函数的局部最大值和最小值。这包括对驻点（Critical Points）的识别，并运用二阶偏导数检验（Hessian 矩阵） 来区分鞍点、局部极大值和局部极小值。此外，拉格朗日乘数法（Lagrange Multipliers） 作为一种强大的约束优化技术，被系统地介绍，它在经济学、物理学约束优化问题中具有不可替代的价值。 第三部分：多重积分——体积与质量的计算 将单变量积分的概念扩展到二维和三维区域，是计算累积量的关键。本部分专注于二重积分和三重积分。 对于二重积分，我们从黎曼和的定义出发，精确地解释了它如何用来计算平面区域上的体积。我们详细分析了直角坐标系下积分区域的描述与积分次序的互换（Fubini's Theorem）。为了应对更复杂的几何形状，本书投入了大量篇幅介绍极坐标系（Polar Coordinates） 及其雅可比行列式，极大地简化了涉及圆形或扇形区域的积分计算。 进入三维空间，三重积分成为计算实体体积、密度函数下的总质量、质心和转动惯量的核心工具。同样，我们引入了柱坐标系（Cylindrical Coordinates） 和球坐标系（Spherical Coordinates），展示了这些坐标变换如何根据问题的几何对称性，将原本繁复的积分转化为易于求解的形式。 第四部分：向量微积分与场论 本部分是多变量微积分中最精妙也最具挑战性的部分，它连接了矢量分析与微分方程的基础。 我们首先定义了向量场（Vector Fields），如流体力学中的速度场或电磁场，并介绍了向量场上的线积分。线积分不仅用于计算粒子在力场中移动所做的功，也是理解流量（Flux）的先导概念。 接着，我们深入探讨了保守场的概念，以及判断一个向量场是否保守的关键工具——旋度（Curl）。旋度的几何意义在于衡量向量场在某点旋转的趋势。 本部分的核心理论是格林公式（Green's Theorem），它建立了平面区域上双重积分与该区域边界上的线积分之间的深刻联系。 在进入三维空间后，我们推广了格林公式，引出了微积分的“终极”定理：斯托克斯定理（Stokes' Theorem） 和散度定理（Divergence Theorem，也称高斯定理）。 斯托克斯定理将曲面上旋度的面积分与该曲面边界上的线积分联系起来，是经典物理学中处理旋转流体的强大工具。 散度定理则建立了穿过闭合曲面的通量（Flux）与曲面内部散度（Divergence）的三重积分之间的关系，是理解流体源汇问题的基础。 教材特色与教学优势 本书的国际公制版本确保了所有示例和练习都采用国际单位制（SI units），更贴合全球工程和科学教育的实践需求。全书的讲解风格注重直观性和几何解释，确保读者不仅学会“如何做”，更能理解“为什么”这样做。 丰富且精心设计的习题贯穿始终，从基础的代数操作到复杂的应用问题，为巩固和检验学习成果提供了充足的资源。关键概念配有详细的图形和图示，帮助学生可视化抽象的四维和多维概念。通过对这些核心概念的系统学习，读者将为后续的微分方程、高等物理、流体力学和复杂系统建模课程打下坚实、无可动摇的数学基础。 本书承诺提供一个全面、严谨且富有启发性的多变量微积分学习体验。

评分☆☆☆☆☆

这本书的国际公制版本，说实话，在某些理论解释上显得有些过于“保守”或“克制”了。它似乎更侧重于形式化的推导和严格的证明，而在直观的几何意义或实际应用场景的阐述上略显不足。举个例子，当它介绍拉格朗日乘数法时，重点完全放在了梯度向量的共线性证明上，但对于“沿着约束曲面寻找极值点”这种几何直觉的描述，却是寥寥数语带过。我发现，我不得不去翻阅其他更侧重于工程应用的教材或在线资源，来弥补这种在“理解其为何如此”上的空缺。一本好的微积分教材，理应在严谨性与直观性之间找到完美的平衡点，但这本书显然更偏向于前者，使得那些希望将数学知识应用于物理或工程领域的读者，会感到理论和实践之间存在一道鸿沟。

评分☆☆☆☆☆

这本书的习题设计实在过于“精英化”了，充满了各种反直觉和需要灵光一现才能解决的怪题。我理解数学学习需要挑战，但挑战和折磨之间只有一线之隔。很多基础练习题的步骤跳跃得非常快，仿佛作者默认读者已经对每一步中间的代数操作了如指掌，完全没有提供足够的“脚手架”。我记得有一道关于泰勒展开式的题目，解答过程直接从一个复杂的函数形式跳跃到了一个简化的连分式，中间缺失了至少五六步关键的因式分解和配方，我花了整整一个下午去逆向推导，才勉强还原出完整的路径。对于那些初次接触微积分，或者数学基础相对薄弱的同学来说，这本书带来的挫败感可能会远大于启发。它更像是为已经掌握了扎实预备知识的“学霸”准备的“挑战手册”，而不是一本普适性的入门教材。

评分☆☆☆☆☆

我是在一个时间非常紧张的学期末接触到这本书的，当时需要快速掌握多变量微积分的基础，而这本书的章节组织逻辑对我来说简直是迷宫。它似乎有一种魔力，总能把最关键的定理和最需要的例题分隔得非常遥远。比如，当你刚学完一个抽象的向量场概念，紧接着出现的习题却要求你用一个半小时前才草草带过的表面积分技巧去解一个看起来无比复杂的实际问题。这种脱节感让我感觉自己像在学一门“孤立知识点”的集合，而不是一门连贯的数学学科。我不得不频繁地跳跃式阅读，前后翻阅几十页才能把一个概念的来龙去脉串起来，这无疑极大地拖慢了我的学习进度，尤其是在期末复习阶段，效率低下带来的焦虑感是难以言喻的。

评分☆☆☆☆☆

这本书的国际度量衡版本在定价上显得极其不合理。考虑到其印刷质量的粗糙程度，以及其内容在某些关键概念解释上的不足，它所要求的价格实在高得离谱。我清楚地知道出版行业的成本构成，但面对一本在国际市场上流通，且在许多大学课程中被强制要求购买的教材，其性价比之低，令人咋舌。每一次翻开它，我总会想到那些为了凑齐教材费而省吃俭用的同学。更讽刺的是，这本书的许多核心内容，在许多更新的、排版更精良的替代品中都能找到，而且价格可能只是其三分之一。这种定价策略，让学习过程本身就充满压力的学生群体，又增添了一份不必要的经济负担，这对于一本旨在普及高等数学知识的工具书来说，实在是一种商业上的不负责任。

评分☆☆☆☆☆

这本教材的排版和印刷质量简直是一场灾难，纸张薄得像蝉翼，油墨总是洇开，尤其是那些复杂的积分符号和希腊字母，看得人头疼欲裂。我记得有一次尝试在图书馆里对着强光看那些微分方程的推导过程，结果眼花了，硬是没看清一个公式的上下标。更别提它的国际公制版本，有些单位的标注方式和我在课堂上习惯的完全不同，让人在做习题时总要多花几秒钟去适应这种“国际化”的表达。说实话，作为一个需要反复查阅和做笔记的学习者来说，这种低劣的物理实体体验，极大地削弱了学习微积分本身的挑战性。我真希望出版商能在这方面多投入一点成本，毕竟这是一本核心的数学参考书，不该如此敷衍了事。我的书架上放着一堆高阶物理和工程学的书，它们的印刷质量都远超此书，让人不禁怀疑这本被寄予厚望的微积分教材，到底经历了怎样的成本控制环节才以这种面貌示人。