# 数学分析1

1．实数理论部分，包括确界原理，函数的概念，基本初等函数的性质。

2．数列极限是极限概念的基础，它包括收敛数列的性质，和数列极限存在的条件。

3．函数极限包括函数极限的概念、性质、存在的条件，两个重要极限和无穷小量和无穷大量。

4．函数的连续性包括：连续的概念、连续函数的性质（保号性、局部有界性、反函数的连续性、四则运算）、初等函数的连续性。

5．导数与微分包括：导数的概念、导数的几何意义、四则运算、复合函数求导数、高阶导数和微分。

6．Lagrange中值定理、Cauchy中值定理、求不定式极限的罗比塔法则、台老公式、极大值极小值、最大值最小值、函数的凸凹性与拐点。

7．实数的完备性包括：区间套定理与Cauchy收敛准则、聚点定理与有限覆盖定理、闭区间上的连续函数的性质。

8．不定积分与定积分。

1. Real number theorem includes the least upper and lower bound, the notation of functions and the properties of the basic fundamental functions.
2. The notation of the sequence of real numbers, the convergence of sequence, monotone sequences and subsequences.
3. The limits of functions include notation, properties, existence, the two important limits, infinity and infinitesimal.
4. The continuity of functions includes continuity, the extreme value theorem, the continuity of inverse function and the properties of continuous functions.
5. The derivative of a real function.
6. Mean value theorems, L’Hospital’s Rule, derivatives of higher order, Taylor’s theorem, maximum and minimum.
7. The nested theorem and Cauchy theorem, the theorem of limit point and finite covering theorem
8. The definition of the integral and criteria for integral bility