本书涵盖了微积分课程的相关知识，全书共分三章：第一章介绍了极限、连续性与致密性，包括数字系统与数学归纳法和基数的简单介绍，并给出了相关的概念和性质；第二章介绍了微分，主要讲述了可微性、高阶偏导数与泰勒定理；第三章介绍了一元与多元积分，给出了有限闭区间上实值函数积分、曲线、弧长和线积分的相关理论。本书需要读者对微积分有一定的了解，是为“有才华”的新生设计的有关分析学的基础教材。

List of Figures
Preface
1 Limits, Continuity, and Compactness
1.1 Number Systems and the Principle of Mathematical Induction
1.2 A Quick Introduction to Cardinal Numbers
1.3 Limits
1.4 Vector Space, Metric Space, Norms, and Inequalities
1.5 Continuous Functions, Open, Closed, and Compact Sets in I~n
2 Differentiation on Rn
2.1 Differentiability on Rn
2.2 Higher Partial Derivatives and Taylor's Theorem
2.3 Maxima and Minima for Real Valued Functions of Several Variables
2.4 The Implicit Function Theorem
3 One and Several Dimensional Integral Calculus
3.1 Brief Review of Integrals of Real-valued Functions Defined on a Finite Closed Interval in R
3.2 Curves, Arc Length, and Line Integrals
3.3 Higher Dimensional Integrals
3.4 Multiple Integrals and their Reduction to One Dimensional Integrals
3.5 Green's Theorem
3.6 Integration on Surfaces
Authors' Biographies
Index
编辑手记