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《海外优秀数学类教材系列丛书:托马斯微积分(第11版)(影印版)(英文)》具有以下几个突出特色：取材于科学和工程领域中的重要应用实例以及配置丰富的习题；对每个重要专题均用语言的、代数的、数值的、图像的方式予以陈述i重视数值计算和程序应用；切实融入数学建模和数学实验的思想和方法；每个新专题都通过清楚的、易于理解的例子启发式地引入，可读性强；配有丰富的教学资源，可用于教师教学和学生学习。

Preface

Pretiminaries

1.1 Real Numbers and the Real Line

1.2 Lines， Circles， and Parabolas

1.3 Functions and Their Graphs

1.4 Identifying Functions； Mathematical Models

1.5 Combining Functions； Shifting and Scaling Graphs

1.6 Trigonometric Functions

1.7 Graphing with Calculators and Computers

QUESTIONS TO GUIDE YOUR REVIEW

PRACTICE EXERCISES

ADDITIONAL AND ADVANCED EXERCISES

Limits and Continuity

2.1 Rates of Change and Limits

2.2 Calculating Limits Using the Limit Laws

2.3 The Precise Definition of a Limit

2.4 One—Sided Limits and Limits at Infinity

2.5 Infinite Limits and Vertical Asymptotes

2.6 Continuity

2.7 Tangents and Derivatives

QUESTIONS TO GUIDE YOUR REVIEW

PRACTICE EXERCISES

ADDITIONAL AND ADVANCED EXERCISES

Differentiation

3.1 The Derivative as a Function

3.2 Differentiation Rules

3.3 The Derivative as a Rate of Change

3.4 Derivatives of Trigonometric Functions

3.5 The Chain Rule and Parametric Equations

3.6 Implicit Differentiation

3.7 Related Rates

3.8 Linearization and Differentials

QUESTIONS TO GUIDE YOUR REVIEW

PRACTICE EXERCISES

ADDITIONAL AND ADVANCED EXERCISES

AppticaUons of Derivatives

4.1 Extreme Values of Functions

4.2 The Mean Value Theorem

4.3 Monotonic Functions and the First Derivative Test

4.4 Concavity and Curve Sketching

4.5 Applied Optimization Problems

4.6 Indeterminate Forms and IgH6pital's Rule

4.7 Newton's Method

4.8 Antiderivatives

QUESTIONS TO GUIDE YOUR REVIEW

PRACTICE EXERCISES

ADDITIONAL AND ADVANCED EXERCISES

Integration

5.1 Estimating with Finite Sums

5.2 Sigma Notation and Limits of Finite Sums

5.3 The Definite Integral

5.4 The Fundamental Theorem of Calculus

5.5 Indefinite Integrals and the Substitution Rule

5.6 Substitution and Area Between Curves

QUESTIONS TO GUIDE YoUR REvIEw

PRACTICE EXERCISES

ADDITIONAL AND ADVANCED EXERCISES

Apptications of Definite Integrats

6.1 Volumes by Slicing and Rotation About an Axis

6.2 Volumes by Cylindrical Shells

6.3 Lengths of Plane Curves

6.4 Moments and Centers of Mass

6.5 Areas of Surfaces of Revolution and the Theorems of Pappus

6.6 Work

6.7 Fluid Pressures and Forces

QUESTIONS TO GUIDE YOUR REVIEW

PRACTICE EXERCISES

ADDITIONAL AND ADVANCED EXERCISES

Transcendentat Functions

7.1 Inverse Functions and Their Derivatives

7.2 Natural Logarithms

7.3 The Exponential Function

7.4 ax and logax

7.5 Exponential Growth and Decay

7.6 Relative Rates of Growth

7.7 Inverse Trigonometric Functions

7.8 Hyperbolic Functions

QUESTIONS TO GLADE YOUR REVIEW

PRACTICE EXERCISES

ADDITIONAL AND ADVANCED EXERCISES

Techniques of Integration 5

8.1 Basic Integration Formulas

8.2 Integration by Parts

8.3 Integration of Rational Functions by Partial Fractions

8.4 Trigonometric Integrals

8.5 Trigonometric Substitutions

8.6 Integral Tables and Comouter Algebra Systems

8.7 Numerical Integration

8.8 Improper Integrals

QUESTIONS TO GUIDE YOUR REVIEW

PRACTICE EXERCISES

ADDITIONAL AND ADVANCED EXERCISES

Further Applications of Integration

9.1 Slope Fields and Separable Differential Equations

9.2 First—Order Linear Differential Equations

9.3 Euler's Method

9.4 Graphical Solutions of Autonomous Differential Equations

9.5 Applications of First—Order Differential Equations

QUESTIONS TO GUIDE YOUR REVIEW

PRACTICE EXERCISES

ADDITIONAL AND ADVANCED EXERCISES

Conic Sections and Polar Coordinates

10.1 Conic Sections and Quadratic Equations

10.2 Classifying Conic Sections by Eccentricity

10.3 Quadratic Equations and Rotations

10.4 Conics and Parametric Equations； The Cycloid

10.5 Polar Coordinates

10.6 Graphing in Polar Coordinates

10.7 Areas and Lengths in Polar Coordinates

10.8 Conic Sections in Polar Coordinates

QUESTIONS TO GUIDE YOUR REVIEW

PRACTICE EXERCISES

ADDITIONAL AND ADVANCED EXERCISES

Infinite Sequences and Series

11.1 Sequences

11.2 Infinite Series

11.3 The Integral Test

11.4 Comparison Tests

11.5 The Ratio and Root Tests _

11.6 Alternating Series， Absolute and Conditional Convergence

11.7 Power Series

11.8 Taylor and Maclaurin Series

11.9 Convergence of Taylor Series； Error Estimates

11.10 Applications of Power Series

11.11 Fourier Series

QUESTIONS TO GUIDE YOUR REVIEW

PRACTICE EXERCISES

ADDITIONAL AND ADVANCED EXERCISES

Vectors and the Geometry of Space

12.1 Three—Dimensional Coordinate Systems

12.2 Vectors

12.3 The Dot Product

12.4 The Cross Product

12.5 Lines and Planes in Space

12.6 Cylinders and Quadric Surfaces

QUESTIONS TO GUIDE YOUR REVIEW

PRACTICE EXERCISES

ADDITIONAL AND ADVANCED EXERCISES

Vector—Valued Functions and Motion in Space

13.1 Vector Functions 906

13.2 Modeling Projectile Motion 920

13.3 Arc Length and the Unit Tangent Vector T 931

13.4 Curvature and the Unit Normal Vector N 936

13.5 Torsion and the Unit Binormal Vector B 943

13.6 Planetary Motion and Satellites 950

QUESTIONS TO GUIDE YOUR REVIEW 959

PRACTICE EXERCISES 960

ADDITIONAL AND ADVANCED EXERCISES 962

Partiat Derivatives

14.1 Functions of Several Variables

14.2 Limits and Continuity in Higher Dimensions

14.3 Partial Derivatives

14.4 The Chain Rule

14.5 Directional Derivatives and Gradient Vectors

14.6 Tangent Planes and Differentials

14.7 Extreme Values and Saddle Points

14.8 Lagrange Multipliers

14.9 Partial Derivatives with Constrained Variables

14.10 Taylor's Formula for Two Variables

QUESTIONS TO GUIDE YOUR REVIEW

PRACTICE EXERCISES

ADDITIONAL AND ADVANCED EXERCISES

Mutipte Integrats

15.1 Double Integrals

15.2 Areas， Moments， and Centers of Mass

15.3 Double Integrals in Polar Form

15.4 Triple Integrals in Rectangular Coordinates

15.5 Masses and Moments in Three Dimensions

15.6 Triple Integrals in Cylindrical and Spherical Coordinates

15.7 Substitutions in Multiple Integrals

QUESTIONS TO GUIDE YOUR REVIEW

PRACTICE EXERCISES

ADDITIONAL AND ADVANCED EXERCISES

Integration in Vector Fietds

16.1 Line Integrals

16.2 Vector Fields， Work， Circulation， and Flux

16.3 Path Independence， Potential Functions， and Conservative Fields

16.4 Green's Theorem in the Plane

16.5 Surface Area and Surface Integrals

16.6 Parametrized Surfaces

16.7 Stokes' Theorem

16.8 The Divergence Theorem and a Unified Theory

QUESTIONS TO GUIDE YOUR RnVIEW

PRACTICE EXERCISES

ADDITIONAL AND ADVANCED EXERCISES

Appendices

A.1 Mathematical Induction

A.2 Proofs of Limit Theorems

A.3 Commonly Occurring Limits

A.4 Theory of the Real Numbers

A.5 Complex Numbers

A.6 The Distributive Law for Vector Cross Products

A.7 The Mixed Derivative Theorem and the Increment Theorem

A.8 The Area of a Parallelogram's Projection on a Plane

A.9 Basic Algebra， Geometry， and Trigonometry Formulas

Answers

Index

A Brief Table of Integrals

Credits

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在线阅读地址：托马斯微积分（上册）在线阅读

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微积分是关于运动和变化的数学。那里有运动或增长，变力做功产生的加速度，那里要用到的数学就是微积分。微积分开创的初期是这样，今天仍然还是这样。

微积分首先是为了满足 16、17 世纪科学家数学方面的要求，本质上说是为了满足力学发展的需要而发明的。微分学处理计算变化率的问题，它使人们能够定义曲线的斜率，计算运动物体的速度和加速度，求得炮弹能够达到其最大射程的发射角，预测何时行星靠得最近或离得最远。积分学处理从函数变化率的信息决定函数自身的问题。它使人们能够从物体现在的位置和作用在物体上力的知识计算该物体将来的位置，求平面上不规则区域的面积，度量曲线的长度，以及求任意空间的体积和质量。

1.阅读课文 你不可能只通过做习题来学会你需要的全部内容和英国逻辑关系，你需要阅读书中有关的段落并一步步把例题解出来。快速阅读在这里不起作用。你是一步步地、合乎逻辑地阅读并探究细节。深刻且技术细节众多的内容所需要的这类阅读要求专注、耐心和实践。

2.做家庭作业 记住以下原则：

（a）只要游客嗯那个，画出示意图。

（b）已一步步紧扣、合乎逻辑的方式写下你的求解过程，就像你是在向别人讲解这个求解过程。

（c）思考一下为什么要在那里设置一道习题。为什么指定要做这道习题？该习题和其他指定的习题有什么关系。

3.使用你的图形计算器和计算机，如果有可能的话。尽可能多地做图形和计算机探究习题，急事是没有指定要你做的题。图形为重要的概念和关系提供洞察和形象的表示。数字能展现模式。图形计算器或计算机可以使你们不费力地去研究手算起来太困难或冗长而确实需要计算的实际问题和例子。

4.每当学完教材的一节试着独立地对关键之处写一个简短的描述。如果你成功了，你肯呢个理解了有关的内容；如果你么有做到，你就会明白你的理解过程中的差距在哪里。

学习微积分是一个过程；它不可能一蹶而就。要有耐心、要锲而不舍、要提问、要和同学讨论概念和共同工作。学习微积分的回报不仅在智力上而且在专业上都将会是令人非常满足的。

第10版更多地强调利用实际数据的建模和应用。因此，在不损害数学的完整性的情形下本书实现了图形、数值、分析的方法和技巧这三者之间逐步完善的平衡.

逐章准备了小测验，这些小测验可以作为基于解题技巧的掌握程度的评估进行在线实施和评分.

We also define surface integrals so we can find the rate that a fluid

flows across a surface.

These more general integrals

are called line integrals, although “curve” integrals might be more descriptive.

书籍介绍

《海外优秀数学类教材系列丛书:托马斯微积分(第11版)(影印版)(英文)》具有以下几个突出特色：取材于科学和工程领域中的重要应用实例以及配置丰富的习题；对每个重要专题均用语言的、代数的、数值的、图像的方式予以陈述i重视数值计算和程序应用；切实融入数学建模和数学实验的思想和方法；每个新专题都通过清楚的、易于理解的例子启发式地引入，可读性强；配有丰富的教学资源，可用于教师教学和学生学习。