课程描述自动化.doc

代数与几何课程编码：08N1120220总 学 时： 60学 分： 3.5先修课程：高中数学授课教师：孟晨辉教 材：线性代数与空间解析几何（第三版）， 高等教育出版社，郑宝东主编课程简介：代数与几何是高等学校功课各专业中十分重要的自然科学基础。其中的线性代数部分主要运用代数方法研究具有线性关系的数学对象，建立相应的理论体系，它具有很强的逻辑性与抽象性；其中的空间解析几何部分主要通过坐标系，建立空间几何图形与方程之间的关系，利用代数理论研究空间几何图形的性质。空间解析几何为线性代数提供背景与示例，线性代数与空间解析几何作为一门课程的两个组成部分，互相渗透，互相支持。本课程系统的介绍线性代数与空间解析几何的基本理论与方法，把线性代数与空间解析几何的求解有机结合。内容包括行列式的定义、计算及其性质；矩阵的代数运算、分块矩阵、矩阵的求秩；向量代数，向量坐标，并在其中讨论几何问题、平面与直线的方程及其相互位置关系；n维向量、向量之间的线性相关性与线性无关性；线性方程组间的结构理论；线性变换与矩阵间的联系；特征值、特征向量、相似变换，矩阵可对角线化的条件和方法；二次型理论、二次型简化、二次曲面及其分类等。评分标准：作业20% 期中考试20% 期末考试60%教学大纲：一、n阶行列式1.1 n阶行列式的概念1.2 行列式的性质1.3 行列式的展开订立1.4 Crammer法则二、矩阵2.1 矩阵的概念2.2 矩阵的运算2.3 可逆矩阵2.4 矩阵的初等变换2.5 矩阵的秩2.6 初等矩阵2.7 分块矩阵的概念及其运算2.8 分块矩阵的初等变换三、几何向量四、n维向量4.1 n维向量的概念及其线性运算4.2 向量组线性相关与线性无关4.3 向量组的秩4.4 向量空间4.5 欧式空间五、线性方程组5.1 线性方程组有解的充要条件5.2 线性方程组解的结构5.3 利用矩阵的初等行变化解线性方程组5.4 线性方程组的几何应用六、特征值、特征向量及相似矩阵6.1 特征值与特征向量6.2 相似矩阵6.3 应用举例七、线性空间与线性变换7.1 线性空间的概念7.2 线性空间的基地、维数与坐标7.3 线性变换八、二次型与二次曲面8.1 实二次型8.2 化实二次型为标准性8.3 正定实二次型8.4 空间中的曲面与曲线8.5 二次曲面Linear Algebra and Analytic GeometryCourse Code: 08N1120220 Hours: 60Credits: 3.5 Prerequisite Course: College-entry level algebra and geometryInstructor: Chenhui MengTextbook:Baodong Zheng, Linear algebra and space analytic geometry, Higher Education PressCourse Description Linear Algebra and Analytic Geometry is one of the significant fundamental courses of nature science. The Linear Algebra mainly applies the algebra method to study the mathematic subjects that have the linear relation and establish corresponding theatrical system. The part of Linear Algebra introduces Basic concepts and techniques of linear algebra; includes systems of linear equations, matrices, determinants, vectors in n-space, and eigenvectors, together with selected applications, such as Markov processes, linear programming, economic models, least squares, and population growth. The Analytic Geometry mainly applies coordinate systems to build the relationship between shapes and equations; and use algebra theory to study the characters of space geometry. The Analytic Geometry provides the background and examples to Linear Algebra. As two parts of the course, the linear algebra and analytic geometry they permeate each other. In addition, this course introduces techniques and applications of ordinary differential equations, including Fourier series and boundary value problems, linear systems of differential equations, and an introduction to partial differential equations. It is designed for engineering majors and other who require a working knowledge of differential equations.Grading: Homework-20% Midterm exam-20% Final exam -60%Syllabus: n order determinant1.1 Basic concepts1.2 Determinant properties1.3 Determinant expansion theorem1.4 Cramer rules matrix 2.1 Basic concepts 2.2 Matrix manipulation 2.3 Invertible matrix 2.4 Elementary transformation of matrices 2.5 Rank of matrix 2.6 Elementary matrix 2.7 Block matrix 2.8 Elementary transformation of block matrices Geometrical vector n dimensional vector 4.1 Concepts 4.2 Linear dependence and linear independence 4.3 Vector set rank 4.4 Vector space 4.5 European space Linear system of equations 5.1 Necessary and sufficient condition for system of linear equations with solution 5.2 System of linear equations solution structure 5.3 Solving system of linear equations using matrix method 5.4 Geometric application for linear system of equations Eigenvalue, eigenvector, and similar matrix 6.1 Eigenvalue and eigenvector 6.2 Similar matrix 6.3 Examples Linear space and linear transformation 7.1 Basic concepts 7.2 Basis, dimensionality, and coordinates 7.3 Linear transformation Quadric form and Quadric surface 8.1 Real quadric form 8.2 Convert real quadric form into normal forms 8.3 Positive definite real quadric form 8.4 Surface and curve in space 8.5 Quadric surface工科数学分析课程编码：08N1120211 08N1120212总 学 时：90+90学 分：5.5+5.5先修课程：高中数学授课教师：白红教 材：工科数学分析（第三版）上册， 工科数学分析（第三版）下册， 高等教育出版社，张宗达主编课程简介： 本课程的教学目的是使学生较系统的理解该课程的基本概念、基本理论、掌握基本方法，为后继课和进一步获取数学知 识奠定必要的数学基础。在传授知识的同时，着重培养学生抽象思维能力、逻辑推理能力、空间想象能力和自学能力，特别是综合运用所学知识去分析问题和解决问题能力。提高学生的素质，培育创新，创业精神。 第一学期讲授的主要内容：函数、极限、连续，一元函数微分学，一元函数积分，导数与定积分的应用；第二学期讲授的主要内容：多元函数微分学，多元函数积分学，无穷级数，常微分方程，复变函数初步、微分几何基础知识。评分标准：作业20% 期中考试20% 期末考试60%Mathematics Analysis for Science and Technology Majors Course Code: 08N1120211 08N1120212 Hours: 90 + 90Credits: 5.5+5.5Instructor: Hong BaiTextbook: Zongda Zhang, Mathematical Analysis for Engineering I II, Higher Education PressCourse Description: Mathematics Analysis for Science and Technology Majors is one of the significant fundamental courses of nature science to every students majoring in engineering. The main content of this course is calculus. The required chapters are function, limits and continuity, derivative and differential, the mean theorems, indefinite integration, definite integration, the approach of derivative and definite integration, differential equation, Derivatives, Integration, the second type curve integral, the second-king surface integral, Vector and infinite series, initial of complex function. The fundamental knowledge of differential geometry is the significant content of the course. Grading: Homework -20% Midterm exam-20% Final exam-60%Syllabus:I. Function 1.1 Basic concepts 1.2 Elementary function 1.3 ExamplesII.Limits and continuity 2.1 Limit of a sequence 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 ExamplesIII. 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 ExamplesIV.Differential mean value theorem 4.1 Differential mean value theorem 4.2 LHospitals rule 4.3 Taylor formula 4.4 ExamplesV 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 ExamplesVI Definite integral 6.1 Concepts 6.2 The fundamental theorem of calculus 6.3 Techniques of definite integral 6.4 Improper integral 6.5 ExamplesVII 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 ExamplesVIII 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 8.7 ExamplesIX 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 ExamplesX 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 ExamplesXI 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 ExamplesXII 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 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 ExamplesXIII 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 13.5 Application of complex functions 13.6 ExamplesXIV 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：1、 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2、 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3、 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3.5 概率密度、均匀分布和指数分布3.6 正态分布4、 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5、 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6、 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7、 参数估计7.1 点估计7.2 区间估计8、 假设检验9、 一元正态线性回归Probability Theory and Mathematical Statistics Course Code: 04N1120050 Hours: 48 Credits: 3.0 Instructor: Yong WangTextbook: Yong Wang, Probability Theory and Mathematical Statistics, Higher Education PressPrerequisite 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 1.2 Calculation of events 1.3 Sample space 1.4 Classical probability 1.5 Geometric probability 1.6 Statistic probabilityII Conditional probability and independence 2.1 Conditional probability 2.2 Multiplication rule 2.3 Total probability formula 2.4 Bayes formula 2.5 Events independence 2.6 Binomial probability formulaIII Random variable and distribution 3.1 Concepts of random variable 3.2 Discrete type random variable: Bernoulli distribution, binomial distribution, Poisson distribution and geometric distribution 3.3 Random variable distribution function 3.4 Continuous random variable 3.5 Probability density, uniform distribution, and exponential distribution 3.6 Normal distributionIV Multiple random variables and their distribution 4.1 Multiple random variables 4.2 Bivariate discrete random variable 4.3 Bivariate continuous random variable 4.4 Independence of random variables 4.5 Bivariate random variable function distribution 4.6 Conditional distributionV Numerical characteristics and limit theorem 5.1 Mathematical expectation 5.2 Variance 5.3 Covariance 5.4 Law of large numbers 5.5 Central-limit theoremVI Mathematical statistics 6.1 Ensemble and sample 6.2 Histogram 6.3 t distribution and F distributionVII Parameter estimation 7.1 Point estimation 7.2 Interval estimationVIII Hypothesis testIX Simple normal linear regression数值分析课程编码： CY120010总 学 时： 64学 分： 4先修课程： 高等数学、计算机基础授课教师： 吴博英教 材： 课程笔记课程描述：数值分析课程研究各种数学问题求解的数值计算方法，讲解如何用计算机解决实际数学问题的方法。学习此课程的目的是掌握基本的数值计算方法。设计求解算法，求出数学问题的近似解。主要内容包括线性方程组的解法（包括直接法和迭代法），插值求职法（拉格朗日插值，牛顿插值，分段低次插值，三次样条插值），函数逼近计算，数值积分与数值微分的近似计算，方程求根的近似解法，以及矩阵特征值与特征向量的计算。Numerical Analysis Course Code: CY120010 Hours: 64Credits: 4 Prerequisite Course: Advanced Mathematics, College Computer Fundamental Instructor: Boying WuTextbook: Class NoteCourse Description Numerical analysis involves the study, development, and analysis of algorithms for obtaining numerical solutions to various mathematical problems. The course introduces students to the algorithms and methods that are commonly needed in scientific computing. The mathematical underpinnings of these methods are emphasized as much as their algorithmic aspects. We believe that students learn and understand numerical methods best by seeing how algorithms are developed from the mathematical theory and then writing and testing computer implementations of them. Some basic contents of this course are linear system solvers, optimization techniques, interpolation and approximation of functions, solving systems of nonlinear equations, eigenvalue problems, least squares, and quadrature; numerical handling of ordinary and partial differential equations. 大学计算机基础OPT2 OPT3 OPT4课程编码： 08C1032340总 学 时： 64学 分： 3.0先修课程： 高中数学、计算机授课教师： 聂兰胜教 材： 大学计算机 高等教育出版社，战德臣、孙大烈等编著课程描述：本课程是计算机和工程专业的一门基础课，介绍计算机发展历程和基本原理，将使学生掌握计算机的基本应用。本课程的主要内容包括：Windows操作系统、办公自动化软件、数据库基础应用、Internet基本应用，并学会简单的网页设计与制作、简单编程方法。并以典型算法类问题和典型系统类问题为例，介绍求解的思维、过程和方法，由算法到系统及综合问题的化解与集成。同时，通过学习本课程，学生将可以熟练掌握科技文章的电子化制作、排版与发布和信息搜索与信息发布的技能。同时本课程也将介绍计算机与信息安全和职业道德的问题。本课程要求实践教学，即在课堂讲授之外，必须配以大量的实际操作训练内容。学生学完本课程后，除掌握基本的计算机理论知识外，更多的是必须能够熟练操作计算机，熟练使用流行的操作系统和文字处理软件，熟练使用Internet平台浏览、搜索信息、收发email等，初步掌握数据库理论知识和简单编程，能够建立静态网站等。评 This course introduces the history, the development and working of computer, including basic concepts in computing and fundamental techniques for solving computational problems. It is intended as a first course for computer science majors and others with a deep interest in computing and engineering. Through this course, student should master the basic approach, including Windows System, Microsoft Office software, and fundamental approach of Data Base, fundamental approach of Internet, simple Web Design and simple programming. Students are required to complete this course accompanied with plenty practices. After this course, they are required to master use computer, such as master how to use popular Microsoft Windows system, to edit words, to browse websites and se arch information, to send and receive email. Moreover, students should understand the theory of data base and simple knowledge of programming, even can establish statistic web sites.Grading: Homework -10% Lab -15% Final exam -75%Syllabus:Introduction1.1 History of computer1.2 History of computer software1.3 Application of computers1.4 Computer technology growing trendComputing theory 2.1 Binary system 2.2 Turing machine 2.3 Von neumann machine 2.4 Computer languages and virtual machine 2.4.1 Machine language 2.4.2 Microprogram language 2.4.3 Assembly language 2.4.4 High level language 2.4.5 Virtual machine 2.5 Information processing Problem solving 3.1 Algorithm problem 3.1.1 Basic concepts 3.1.2 Setting the mathematical model 3.1.3 Building the data structure 3.1.4 Control structure and flow diagram 3.1.5 Method to solve algorithm problem 3.1.6 Programming language 3.1.7 Program implementation of algorithm problem 3.1.8 Simulation and analysis of algorithm 3.1.9 Algorithm complexity 3.2 System problem 3.2.1 Basic concepts 3.2.2 Modeling 3.2.3 Setting the program model 3.2.4 Program modules implementation 3.2.5 Program system implementation 3.2.6 Program system operation 3.2.7 Software architecture 3.2.8 System reliability Operating system 4.1 Concepts and functions 4.2 Files and disks management 4.3 Peripheral equipment management 4.4 Startup, operate, and close 4.5 Graphical user interface operating system 4.6 The command line type interactive interface operating system Algorithm programming 5.1 Program design process 5.2 Program development environment 5.3 Programming language 5.4 Arithmetic statement and program designing 5.5 Event driven procedure and visualizing program 5.6 Visualizing programming using Visual Basic Editing science papers Information retrieval, exchange and release 7.1 Computer networks 7.2 Internet and its basic service 7.3 Search engine and information releasing 7.4 Internet emerging services Information management and database 8.1 Database concepts 8.2 Relational model and Relational database 8.3 Structured Query Language 8.4 Relational database designing Computer and information security 9.1 Computer and information security 9.2 Common security threats 9.3 Computer and information