高等数学(上英文版高等院校双语教学规划教材)

《高等数学》是为响应东南大学国际化需要，根 据国家教育部非数学专业数学基础课教学指导分委员 会制定的工科类本科数学基础课程教学基本要求，并 结合东南大学数学系多年教学改革实践经验编写的全 英文教材。全书分为上、下两册，内容包括极限、一 元函数微分学、一元函数积分学、常微分方程、级数 、向鼍代数与空间解析几何、多元函数微分学、多元 函数积分学、向量场的积分、复变函数等十个章节。 本书是上册，共四章。 本书可作为高等理工科院校非数学类专业本科生 学习高等数学的英文教材，也可供其他专业选用和社 会读者阅读。

Chapter 1 Limits 1.1 The Concept of Limits and its Properties 1.1.1 Limits of Sequence 1.1.2 Limits of Functions 1.1.3 Properties of Limits Exercise 1.1 1.2 Limits Theorem 1.2.1 Rules for Finding Limits 1.2.2 The Sandwich Theorem 1.2.3 Monotonic Sequence Theorem 1.2.4 The Cauchy Criterion Exercise 1.2 1.3 Two Important Special Limits Exercise 1.3 1.4 Infinitesimal and Infinite 1.4.1 Infinitesimal 1.4.2 Infinite Exercise 1.4 1.5 Continuous Function 1.5.1 Continuity 1.5.2 Discontinuity Exercise 1.5 1.6 Theorems about Continuous Function on a Closed Interval Exercise 1.6 Review and Exercise Chapter 2 Differentiation 2.1 The Derivative Exercise 2.1 2.2 Rules for Fingding the Derivative 2.2.1 Derivative of Arithmetic Combination 2.2.2 The Derivative Rule for Inverses 2.2.3 Derivative of Composition 2.2.4 Implicit Differentiation 2.2.5 Parametric Differentiation 2.2.6 Related Rates of Change Exercise 2.2 2.3 Higher-Order Derivatives Exercise 2.3 2.4 Differentials Exercise 2.4 2.5 The Mean Value Theorem Exercise 2.5 2.6 L'Hospital's Rule Exercise 2.6 2.7 Taylor's Theorem Exercise 2.7 2.8 Applications of Derivatives 2.8.1 Monotonicity 2.8.2 Local Extreme Values 2.8.3 Extreme Values