《微積分 I（雙語版）》是“靠前本科學術互認課程  數學基礎繫列教材”之一冊，是根據“靠前本科學術互認課程”數學基礎課程的要求及培養模式進行編寫的“微積分”雙語課程教材。本書以適用、夠用為原則，切合學生實際，在體繫完整的基礎上，對通常的 “微積分”課程內容進行適當的調整，強調數學思想方法及應用。本書敘述簡明易懂、由淺入深、條理清晰、重點突出，便於教師教學與學生自學。

●目錄Chapter 1Functions章函數1.1Functions and Their Graphs1.1函數及其圖像1. The Domain and the Range of a Function1. 函數的定義域和值域2. The Graph of a Function2. 函數的圖像 3. The Vertical Line Test for a Function3. 函數的垂直線測試4. Examples of Functions4. 函數的例子1.2The Spe Properties of Functions1.2函數的特性1. The Boundness of a Function1. 函數的有界性2. The Monotonicity of a Function2. 函數的單調性3. The Symmetry of a Function3. 函數的對稱性4. The Periodicity of a Function4. 函數的周期性1.3The Operations of Functions1.3函數的運算1. The Arithmetic of Functions1. 函數的四則運算2. The Composition of Functions2. 函數的復合3. The Transformations of Functions3. 函數的變換1.4Elementary Functions1.4初等函數1. Basic Elementary Functions1. 基本初等函數2. Elementary Functions2. 初等函數 Exercises 1 習題1Chapter 2Limits第2章極限2.1The Limit of a Sequence2.1數列的極限1. The Definition of the Convergent Sequence1. 收斂數列的定義2. The Properties of a Convergent Sequence2. 收斂數列的性質2.2The Limit of a Function2.2函數的極限1. The Limit of a Function as x→x01. 函數在x→x0時的極限2. Onesided Limits2. 單側極限3. The Limit of a Function as x→ 3. 函數在x→ 時的極限4. Infinite Limits4. 無窮極限5. The Properties of Limits5. 極限的性質2.3Limit Laws2.3極限運算法則2.4Limit Existence Rules and Two Important Limits2.4極限存在準則和兩個重要極限2.5The Continuity of Functions2.5函數的連續性1. Continuity at a Point 1. 在一點處的連續性2. Several Common Types of Discontinuities2. 間斷點的幾種常見類型3. Continuity on an Interval3. 區間上的連續性4. The Operations of Continuous Functions4. 連續函數的運算5. The Properties of Continuous Functions on a Closed Interval5. 閉區間上連續函數的性質2.6Infinitesimals and Infinitys 2.6無窮小量和無窮大量1. Infinitesimals1. 無窮小量2. Infinitys2. 無窮大量3. Compare of Infinitesimals 3. 無窮小量的比較 Exercises 2 習題2Chapter 3The Derivative and the Differential第3章導數和微分3.1The Concept of the Derivative3.1導數的概念1. Introducing Examples1. 引例2. The Derivative of Function at a Point2. 函數在一點處的導數3. Onesided Derivatives3. 單側導數4. The Derivative of a Function4. 函數的導數5. Relationship Between Differentiability and Continuity 5. 可導與連續的關繫3.2The Rules for Finding Derivatives3.2求導法則1. The Constant ltiple Rule1. 常數乘法法則2. The Sum Rule2. 和法則3. The Difference Rule3. 差法則4. The Product Rule4. 乘積法則5. The Quotient Rule5. 商法則6. The Rule for the Derivative of an Inverse Function6. 反函數求導法則7. The Derivative Formulas of Basic Elementary Functions7. 基本初等函數的導數公式8. The Chain Rule8. 鏈式法則3.3Higherorder Derivatives3.3高階導數3.4The Derivatives of Implicit Functions and Functions Determined by Parameter Equations3.4隱函數及由參數方程確定的函數的導數1. The Derivative of an Implicit Function1. 隱函數的導數2. The Derivative of a Function Determined by a Parameter Equation2. 由參數方程確定的函數的導數3.5The Differential and the Approximation3.5微分和近似1. The Definition of the Differential1. 微分的定義2. The Rules of the Differential2. 微分法則3. The Differential Formulas of Basic Elementary Functions3. 基本初等函數的微分公式4. The Linear Approximation of a Function4. 函數的線性近似 Exercises 3 習題3Chapter 4Applications of the Derivative第4章導數的應用4.1The Mean Value Theorem4.1微分中值定理4.2The L’Hospital Rule4.2洛必達法則4.3The Criterion of the Monotonicity of Functions 4.3函數的單調性判別法1. The First Derivative and Monotonicity1. 函數的一階導數與單調性2. The Second Derivative and Concavity2. 二階導數和凹性4.4Maxima and Minima4.4優選值和最小值1. The Existence Question1. 存在性問題2. Where Do Extreme Values Occur?2. 最值在哪裡出現？3. How to Find Extreme Values?3. 如何求最值?4.5Local Extrema and Local Extrema on Open Intervals4.5局部極值與開區間上的局部極值1. Where Do Local Extreme Values Occur?1. 局部極值存在於何處?2. Extrema on an Open Interval2. 開區間上的最值 4.6Graphing Functions4.6作函數的圖像 Exercises 4 習題4Chapter 5The Indefinite Integral第5章不定積分5.1The Concept and the Properties of the Indefinite Integral5.1不定積分的概念與性質1. The Concepts of the Primitive Function and the Indefinite Integral1. 原函數與不定積分的概念2. Basic Formulas of Integrals2. 基本積分公式3. The Properties of the Indefinite Integral3. 不定積分的性質5.2Integration by Substitution5積分法1. The Substitution Rule 11法2. The Substitution Rule 2 2. 法5.3Integration by Parts5.3分部積分法5.4The Indefinite Integral of the Rational Function5.4有理函數的不定積分1. The Indefinite Integral of the Rational Function1. 有理函數的不定積分2. The Indefinite Integral of the Rational Function with Trigonometric Function2. 三角函數有理式的不定積分3. The Indefinite Integral of the Simple Irrational Function3. 簡單無理函數的不定積分 Exercises 5 習題5Chapter 6The Definite Integral第6章定積分6.1The Concept and the Properties of the Definite Integral6.1定積分的概念與性質1. Examples of the Definite Integral1. 定積分問題舉例2. The Definition of the Definite Integral2. 定積分的定義3. The Geometric Significance of the Definite Integral3. 定積分的幾何意義4. The Properties of the Definite Integral4. 定積分的性質6.2The Fundamental Formula of Calculus6.2微積分基本公式1. The Function of Integral Upper Limit and Its Derivative1. 積分上限函數及其導數2. The NewtonLeibniz Formula2. 牛頓萊布尼茨公式6.3Definite Integration by Substitution and Parts6.3定積法和分部積分法1. Definite Integration by Substitution1. 定積法2. Definite Integration by Parts2. 定積分的分部積分法6.4The Improper Integral6.4反常積分1. The Improper Integral of Infinite Limit1. 無窮限的反常積分2. The Improper Integral of the Unbounded Function2. 無界函數的反常積分6.5Applications of the Definite Integral6.5定積分的應用1. The Infinitesimal Method1法2. Applications in Geometry 2. 在幾何中的應用3. Applications in Economics3. 在經濟中的應用4. Application in Physics 4. 在物理中的應用 Exercises 6 習題6

    《微積分 I（雙語版）》是根據“靠前本科學術互認課程”（ISEC）項目對高等數學繫列課程的要求，同時結合ISEC項目培養模式進行編寫的“微積分”雙語教材。全書共分5章，內容包括：函數、極限、導數和微分、導數的應用、不定積分、定積分等。在內容選擇上，既考慮到ISEC學生未來學習和發展的需要，又兼顧學生數學學習的實際情況，以適用、夠用為原則，切合學生實際，在體繫完整的基礎上，對通常的 “微積分”課程內容進行適當的調整，注重明晰數學思想與方法，強調數學知識的應用;在內容闡述上，盡量以案例模式引入，由淺入深，由易到難，循序漸進地加以展開，並且盡量使重點突出，難點分散，便於學生對知識的理解和掌握；在內容呈現上，以英文和中文兩種文字進行編寫，分左、右欄對應呈現，方便學生學習與理解。    本書既可作為ISEC項目培等

程曉亮、王洋 著