高等数学(下英文版高等院校双语教学规划教材)

本书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、向量代 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 学习高等数学课程的英文教材，也可供其他专业选用 和社会读者阅读。

Chapter 5 Infinite Series 5.1 Infinite Series 5.1.1 The Concept of Infinite Series 5. 1.2 Conditions for Convergence 5.1.3 Properties of Series Exercise 5.1 5.2 Tests for Convergence of Positive Series Exercise 5.2 5.3 Alternating Series, Absolute Convergence, and Conditional Convergence 5.3. 1 Alternating Series 5. 3.2 Absolute Convergence and Conditional Convergence Exercise 5. 3 5. 4 Tests for Improper Integrals 5.4. 1 Tests for the Improper Integrals: Infinite Limits of Integration 5.4. 2 Tests for the Improper Integrals: Infinite Integrands 5.4. 3 The Gamma Function Exercise 5.4 5.5 Infinite Series of Functions 5.5.1 General Definitions 5.5.2 Uniform Convergence of Series 5. 5. 3 Properties of Uniformly Convergent Functional Series Exercise 5.5 5.6 Power Series 5.6.1 The Radius and Interval of Convergence 5.6. 2 Properties of Power Series 5.6. 3 Expanding Functions into Power Series Exercise 5. 6 5.7 Fourier Series 5.7. 1 The Concept of Fourier Series 5.7. 2 Fourier Sine and Cosine Series 5.7. 3 Expanding Functions with Arbitrary Period Exercise 5. 7 Review and Exercise …… Chapter 6 Vectors and Analytic Geometry in Space Chapter 7 Multivariable Functions and Partial Derivatives Chapter 8 Multiple Integrals Chapter 9 Integration in Vectors Field Chapter 10 Complex Analysis Solutions to selected problem