《微积分 I（双语版）》是根据“靠前本科学术互认课程”（ISEC）项目对高等数学系列课程的要求，同时结合ISEC项目培养模式进行编写的“微积分”双语教材。全书共分5章，内容包括：函数、极限、导数和微分、导数的应用、不定积分、定积分等。在内容选择上，既考虑到ISEC学生未来学习和发展的需要，又兼顾学生数学学习的实际情况，以适用、够用为原则，切合学生实际，在体系完整的基础上，对通常的 “微积分”课程内容进行适当的调整，注重明晰数学思想与方法，强调数学知识的应用;在内容阐述上，尽量以案例模式引入，由浅入深，由易到难，循序渐进地加以展开，并且尽量使重点突出，难点分散，便于学生对知识的理解和掌握；在内容呈现上，以英文和中文两种文字进行编写，分左、右栏对应呈现，方便学生学习与理解。    本书既可作为ISEC项目培养模式下“微积分”课程的教材，也可作为普通高等院校“微积分”课程的教学参考书，特别是以英文和中文两种语言学习和理解“微积分”的参考资料。    为方便教学，作者为任课教师提供相关的电子资源，具体事宜可通过电子邮件与作者联系，邮箱地址：chengxiaoliang92@163.com.

    程晓亮，吉林师范大学数学学院副教授，硕士生导师，在我社出版多部教材。王洋：吉林师范大学数学学院教师，一直工作在“靠前本科学术互认课程”中“微积分”课程的教学线，具有丰富的教学经验。

目录Chapter 1Functions章函数1.1Functions and Their Graphs1.1函数及其图像1. The Domain and the Range of a Function1. 函数的定义域和值域2. The Graph of a Function2. 函数的图像 3. The Vertical Line Test for a Function3. 函数的垂直线测试4. Examples of Functions4. 函数的例子1.2The Spe Properties of Functions1.2函数的特性1. The Boundness of a Function1. 函数的有界性2. The Monotonicity of a Function2. 函数的单调性3. The Symmetry of a Function3. 函数的对称性4. The Periodicity of a Function4. 函数的周期性1.3The Operations of Functions1.3函数的运算1. The Arithmetic of Functions1. 函数的四则运算2. The Composition of Functions2. 函数的复合3. The Transformations of Functions3. 函数的变换1.4Elementary Functions1.4初等函数1. Basic Elementary Functions1. 基本初等函数2. Elementary Functions2. 初等函数 Exercises 1 习题1Chapter 2Limits第2章极限2.1The Limit of a Sequence2.1数列的极限1. The Definition of the Convergent Sequence1. 收敛数列的定义2. The Properties of a Convergent Sequence2. 收敛数列的性质2.2The Limit of a Function2.2函数的极限1. The Limit of a Function as x→x01. 函数在x→x0时的极限2. Onesided Limits2. 单侧极限3. The Limit of a Function as x→∞3. 函数在x→∞ 时的极限4. Infinite Limits4. 无穷极限5. The Properties of Limits5. 极限的性质2.3Limit Laws2.3极限运算法则2.4Limit Existence Rules and Two Important Limits2.4极限存在准则和两个重要极限2.5The Continuity of Functions2.5函数的连续性1. Continuity at a Point 1. 在一点处的连续性2. Several Common Types of Discontinuities2. 间断点的几种常见类型3. Continuity on an Interval3. 区间上的连续性4. The Operations of Continuous Functions4. 连续函数的运算5. The Properties of Continuous Functions on a Closed Interval5. 闭区间上连续函数的性质2.6Infinitesimals and Infinitys 2.6无穷小量和无穷大量1. Infinitesimals1. 无穷小量2. Infinitys2. 无穷大量3. Compare of Infinitesimals 3. 无穷小量的比较 Exercises 2 习题2Chapter 3The Derivative and the Differential第3章导数和微分3.1The Concept of the Derivative3.1导数的概念1. Introducing Examples1. 引例2. The Derivative of Function at a Point2. 函数在一点处的导数3. Onesided Derivatives3. 单侧导数4. The Derivative of a Function4. 函数的导数5. Relationship Between Differentiability and Continuity 5. 可导与连续的关系3.2The Rules for Finding Derivatives3.2求导法则1. The Constant Multiple Rule1. 常数乘法法则2. The Sum Rule2. 和法则3. The Difference Rule3. 差法则4. The Product Rule4. 乘积法则5. The Quotient Rule5. 商法则6. The Rule for the Derivative of an Inverse Function6. 反函数求导法则7. The Derivative Formulas of Basic Elementary Functions7. 基本初等函数的导数公式8. The Chain Rule8. 链式法则3.3Higherorder Derivatives3.3高阶导数3.4The Derivatives of Implicit Functions and Functions Determined by Parameter Equations3.4隐函数及由参数方程确定的函数的导数1. The Derivative of an Implicit Function1. 隐函数的导数2. The Derivative of a Function Determined by a Parameter Equation2. 由参数方程确定的函数的导数3.5The Differential and the Approximation3.5微分和近似1. The Definition of the Differential1. 微分的定义2. The Rules of the Differential2. 微分法则3. The Differential Formulas of Basic Elementary Functions3. 基本初等函数的微分公式4. The Linear Approximation of a Function4. 函数的线性近似 Exercises 3 习题3Chapter 4Applications of the Derivative第4章导数的应用4.1The Mean Value Theorem4.1微分中值定理4.2The L’Hospital Rule4.2洛必达法则4.3The Criterion of the Monotonicity of Functions 4.3函数的单调性判别法1. The First Derivative and Monotonicity1. 函数的一阶导数与单调性2. The Second Derivative and Concavity2. 二阶导数和凹性4.4Maxima and Minima4.4最大值和最小值1. The Existence Question1. 存在性问题2. Where Do Extreme Values Occur?2. 最值在哪里出现？3. How to Find Extreme Values?3. 如何求最值?4.5Local Extrema and Local Extrema on Open Intervals4.5局部极值与开区间上的局部极值1. Where Do Local Extreme Values Occur?1. 局部极值存在于何处?2. Extrema on an Open Interval2. 开区间上的最值 4.6Graphing Functions4.6作函数的图像 Exercises 4 习题4Chapter 5The Indefinite Integral第5章不定积分5.1The Concept and the Properties of the Indefinite Integral5.1不定积分的概念与性质1. The Concepts of the Primitive Function and the Indefinite Integral1. 原函数与不定积分的概念2. Basic Formulas of Integrals2. 基本积分公式3. The Properties of the Indefinite Integral3. 不定积分的性质5.2Integration by Substitution5.2换元积分法1. The Substitution Rule 11. 换元法2. The Substitution Rule 2 2. 第二换元法5.3Integration by Parts5.3分部积分法5.4The Indefinite Integral of the Rational Function5.4有理函数的不定积分1. The Indefinite Integral of the Rational Function1. 有理函数的不定积分2. The Indefinite Integral of the Rational Function with Trigonometric Function2. 三角函数有理式的不定积分3. The Indefinite Integral of the Simple Irrational Function3. 简单无理函数的不定积分 Exercises 5 习题5Chapter 6The Definite Integral第6章定积分6.1The Concept and the Properties of the Definite Integral6.1定积分的概念与性质1. Examples of the Definite Integral1. 定积分问题举例2. The Definition of the Definite Integral2. 定积分的定义3. The Geometric Significance of the Definite Integral3. 定积分的几何意义4. The Properties of the Definite Integral4. 定积分的性质6.2The Fundamental Formula of Calculus6.2微积分基本公式1. The Function of Integral Upper Limit and Its Derivative1. 积分上限函数及其导数2. The NewtonLeibniz Formula2. 牛顿莱布尼茨公式6.3Definite Integration by Substitution and Parts6.3定积分的换元法和分部积分法1. Definite Integration by Substitution1. 定积分的换元法2. Definite Integration by Parts2. 定积分的分部积分法6.4The Improper Integral6.4反常积分1. The Improper Integral of Infinite Limit1. 无穷限的反常积分2. The Improper Integral of the Unbounded Function2. 无界函数的反常积分6.5Applications of the Definite Integral6.5定积分的应用1. The Infinitesimal Method1. 微元法2. Applications in Geometry 2. 在几何中的应用3. Applications in Economics3. 在经济中的应用4. Application in Physics 4. 在物理中的应用 Exercises 6 习题6