2.2 Limit of a function

2.3 Limit properties, infinitesimal and infinite 2.4 Limit algorithm

2.5 Criteria of limit existence 2.6 Infinitesimal comparison 2.7 Continuity of a function 2.8 Examples

III. Derivative and differential 3.1 Basic concepts

3.2 Arithmetic rules for derivative and differential 3.3 Other rules for calculating derivative 3.4 Higher order derivative 3.5 Differential 3.6 Examples

IV.Differential mean value theorem 4.1 Differential mean value theorem 4.2 L’Hospital’s rule 4.3 Taylor formula 4.4 Examples V Indefinite integral 5.1 Indefinite integral

5.2 Techniques of integration ----- integration by substitution 5.3 Techniques of integration ---- integration by parts 5.4 Techniques of integration for special functions 5.5 Examples VI Definite integral 6.1 Concepts

6.2 The fundamental theorem of calculus 6.3 Techniques of definite integral 6.4 Improper integral 6.5 Examples

VII Applications of integration

7.1 Extreme, maximum and minimum values 7.2 Graphing with calculus and calculators

7.3 Arc length of a curve, differential of arc length, and curvature 7.4 Application of definite integral 7.5 Examples

VIII Differential equations 8.1 Concepts

8.2 First order differential equation

8.3 Integrable higher order differential equation

8.4 Linear differential equations and their general solution

8.5 Constant coefficient homogeneous linear differential equations 8.6 Constant coefficient nonhomogeneous linear differential equations

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8.7 Examples

IX Multivariable differential calculus 9.1 Concepts

9.2 Partial derivative 9.3 Complete differential

9.4 Derivation for compound function 9.5 Derivation for implicit function

9.6 Geometric application for partial derivative

9.7 First order Taylor formula and extreme values for multivariable function 9.8 Directional derivative and gradient 9.9 Examples

X Multivariable integral calculus 10.1 Riemann integral 10.2 Double integral 10.3 Triple integral

10.4 The first type curve integral 10.5 The first type surface integral 10.6 Application of Riemann integral 10.7 Examples

XI The second type curve integral and surface integral, vector field 11.1 Vector field

11.2 The second type curve integral

11.3 Green formula, plane velocity field circular rector and rotation 11.4 Path irrelevant, conservative field 11.5 The second type surface integral 11.6 Gauss formula, flux and divergence

11.7 Stokes’ theorem, circular rector and rotation 11.8 Examples XII Infinite series

12.1 Convergence and divergence of infinite series

12.2 Convergence and divergence criteria of positive series 12.3 Alternating series, absolute convergence

12.4 Convergence and divergence criteria of improper integral and Г function 12.5 Series with function terms, uniform convergence 12.6 Power series

12.7 Power series expansion for functions 12.8 Application of power series 12.9 Fourier series 12.10 Examples

XIII Complex variables functions

13.1 Complex number and complex variable functions 13.2 Analytic function

13.3 Complex function integral

13.4 Complex function series representation

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13.5 Application of complex functions 13.6 Examples

XIV Differential geometry 14.1 Vector functions

14.2 Introduction to curve theory

14.3 The first fundamental form of curve theory 14.4 The second fundamental form of curve theory 14.5 Geodesic 14.6 Examples

概率论与数理统计

课程编码：04N1120050 总 学 时：48 学 分：3

先修课程：线性代数 授课教师：王勇 教 材：《概率论与数理统计》，王勇主编，高等教育出版社 课程简介：

通过分析简单的随机现象，概率理论提出了统计模式的现象。概率理论也是统计的基本理论。通过本课程的学习，是学生掌握处理随机现象的基本思想方法，掌握概率论和数理统计的基本知识，培养学生运用概率统计方法提高分析和解决实际问题的能力。 评分标准：作业——20% 期中考试——20% 期末考试——60% 教学大纲：

一、随机事件与概率

1.1随机事件

1.2 事件的关系与运算 1.3 样本空间 1.4 古典概率 1.5 几何概率 1.6 统计概率 二、条件概率与独立性

2.1 条件概率 2.2 乘法定理 2.3 全概率公式 2.4 贝叶斯公式 2.5 事件的独立性 2.6 二项概率公式 三、随机变量及其分布

3.1 随机变量的概念

3.2 离散型随机变量：伯努利分布、二项分布、泊松分布和几何分布 3.3 随机变量的分布函数 3.4 连续型随机变量

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3.5 概率密度、均匀分布和指数分布 3.6 正态分布

四、多维随机变量及其分布

4.1 多维随机变量

4.2 二维离散型随机变量 4.3 二维连续型随机变量 4.4 随机变量的独立性

4.5 二维随机变量函数的分布 4.6 条件分布

五、随机变量的数字特征与极限定理

5.1 数学期望 5.2 方差 5.3 协方差 5.4 大数定律 5.5 中心极限定理 六、数理统计的基本概念

6.1 总体与样本 6.2 直方图

6.3 t分布和F分布 七、参数估计

7.1 点估计 7.2 区间估计 八、假设检验

九、一元正态线性回归

Probability Theory and Mathematical Statistics

Course Code: 04N1120050 Hours: 48 Credits: 3.0

Instructor: Yong Wang

Textbook: Yong Wang, Probability Theory and Mathematical Statistics, Higher Education Press Prerequisite Course: Linear Algebra and Analytic Geometry Course Description:

By analyzing those simple random phenomena, probability theory comes up with the statistical patterns of random phenomena. Probability theory is also the fundamental theory of statistics. In this course the students learn the basic concepts and methods to process the random phenomena and grasp the basic knowledge of Probability Theory & Mathematical Statistics, and therefore improve their ability to analyze and solve problems with probability statistics.

Grading: Homework-----------------------20% Midterm exam-------------------20% Final exam-------------------------60% Syllabus:

I Random event and probability 1.1 Random event

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