高等数学建模II教学大纲AdvancedMathematicalSubject SyllabusModelling II一、课程信息SubjectInformation课程编号：开课学期：2EQV-CS-33130Subject IDSemester课程分类：所属课群：专业教育PA专业基础MFSectionCategory课程学分：总学时/周：696/16Credit PointsTotal Hours/Weeks理论学时：实验学时：960LECT. HoursEXP. HoursPBL学时：实践学时/周：00PBL HoursPRAC.Hours/Weeks东北大学悉尼智能科技学院适用专业：开课学院：Sydney SmartCST/CECollegeTechnology CollegeStreamNortheasternUniversity课程属性课程模式：必修Compulsory互认EQVPatternMode中方课程协调人：李晓奇成绩记载方式：百分制MarksNEU CoordinatorLiQiaoqiResult Type先修课程：无NoneRequisites1.Mo Huixia, LiXiaohua,Yuan Jianhua, Yuan Jianhua,AiWenbao,Zhu Ping, Advanced Mathematics (I) & (Il), 2nd Edition, Beijing英文参考教材UniversityofPostsandTelecommunicationsPress,2018.ENTextbooks2.J.L.Devore, Probability and Statistics for Engineering and theScience, Beijing CENGAGE, 2015.同济大学数学系，高等数学（第七版）上、下册，高等教育出版社，2014中文参考教材浙江大学数学系，概率论与数理统计（第五版），高等教育出版社，CN Textbooks2007教学资源https://sstc.cloudcampus.com.cn/course/view.php?id=9Resources李晓奇课程负责人(撰写人)：提交日期：3/1/2023Subject DirectorLiQiaoqiSubmitted Date杜瑞燕、郭静梅、李晓奇任课教师(含负责人)：Taught byDu Ruiyan, Guo Jingmei, Li Xiaoqi1/15
1 / 15 高等数学建模 II 教学大纲 Subject Syllabus Advanced Mathematical Modelling II 一、课程信息 Subject Information 课程编号: Subject ID EQV-CS-33130 开课学期: Semester 2 课程分类: Category 专业教育 PA 所属课群: Section 专业基础 MF 课程学分: Credit Points 6 总学时/周: Total Hours/Weeks 96/16 理论学时: LECT. Hours 96 实验学时: EXP. Hours 0 PBL 学时: PBL Hours 0 实践学时/周: PRAC. Hours/Weeks 0 开课学院: College 东北大学 悉尼智能科技学院 Sydney Smart Technology College Northeastern University 适用专业: Stream CST/CE 课程属性: Pattern 必修 Compulsory 课程模式: Mode 互认 EQV 中方课程协调人: NEU Coordinator 李晓奇 Li Qiaoqi 成绩记载方式: Result Type 百分制 Marks 先修课程: Requisites 无 None 英文参考教材: EN Textbooks 1. Mo Huixia, Li Xiaohua, Yuan Jianhua, Yuan Jianhua, Ai Wenbao, Zhu Ping, Advanced Mathematics (I) & (II), 2nd Edition, Beijing University of Posts and Telecommunications Press, 2018. 2. J.L. Devore, Probability and Statistics for Engineering and the Science, Beijing CENGAGE, 2015. 中文参考教材: CN Textbooks 同济大学数学系,高等数学(第七版)上、下册, 高等教育出版社, 2014 浙江大学数学系,概率论与数理统计(第五版), 高等教育出版社, 2007 教学资源: Resources https://sstc.cloudcampus.com.cn/course/view.php?id=9 课程负责人(撰写人): Subject Director 李晓奇 Li Qiaoqi 提交日期: Submitted Date 3/1/2023 任课教师(含负责人): Taught by 杜瑞燕、郭静梅、李晓奇 Du Ruiyan, Guo Jingmei, Li Xiaoqi
审核人：批准人：韩鹏史闻博Checked byApproved by批准日期：3/3/2023Approved Date2 /15
2 / 15 审核人: Checked by 韩鹏 批准人: Approved by 史闻博 批准日期: Approved Date 3/3/2023
二、教学目标SubjectLearningObjectives(SLOs)注：毕业要求及指标点可参照悉尼学院本科生培养方案，可根据实际情况增减行数Note: GA and index can be referred from undergraduate program in SSTC website. Please add/reduce lines based on subject高等数学建模是理工科专业课程的基础，通过学习极限、微分、积分等重要概念，为学生学习其它学科以至于专业课程打下扎实基础。培养学生较强的动手能力，以及思维的逻辑性、严谨性、创新性，以及利用数学原理和方法解决实际问题的意识、兴趣和能力。培养学生掌握高等数学的基本理论和方法，尤其是思维方式，掌握知识技能的同时发展创造能力。Advancedmathematical modeling is the foundation of science and整体目标：engineering courses. By leaming the important concepts of limit,OverallObjectivedifferential and integral, it can lay a solid foundation for students tolearn other subjects and even professional courses.To cultivatestudents' strong practical ability, logical, rigorous and innovativethinking, as well as the consciousness, interest and ability of solvingpractical problems by using mathematical principles and methods.Cultivatestudentstomaster thebasictheoriesandmethods ofhighermathematics,especiallythewayofthinking,masterknowledgeandskills,and develop creative ability at the same time具有扎实的专业基础与学科特长，系统掌握统计与数据分析、智能仿真建模技术、量化管理优化技术、试验设计与分析、项目管理与决策及其相关领域的专门知识与技能。A solid professional foundation and competency, systematical1-1mastery ofthe specialized knowledge and skills in statistics anddata analysis, intelligent simulation modeling technology,quantitativemanagementoptimizationtechnologyexperimental design and analysis,projectmanagementanddecision-making具有扎实的专业基础与学科特长，系统掌握信息通信系统、项目管理与决策及其相关领域专门知识与技能。Excellent engineering literacy, outstanding practical sklls in（1）专业目标：information technology,and capable of creatively solving1-2ProfessionalAbilitycomplexengineeringproblemsininformationandcommunication and related fields through scientific andtechnological theories and engineering practical methods, aswell as the ability of doing academic cutting-edge projectresearch具有扎实的专业基础与学科特长，系统掌握大数据与人工智能系统、项目管理与决策及其相关领域专门知识与技能。Excellent engineering literacy, outstanding practical skills ininformation technology,and capable of creatively solving1-3complex engineering problems in computer science and relatedfields through scientific and technological theories andengineering practical methods, as well as the ability of doingacademic cutting-edge project research3/15
3 / 15 二、教学目标 Subject Learning Objectives (SLOs) 注：毕业要求及指标点可参照悉尼学院本科生培养方案，可根据实际情况增减行数 Note: GA and index can be referred from undergraduate program in SSTC website. Please add/reduce lines based on subject. 整体目标: Overall Objective 高等数学建模是理工科专业课程的基础，通过学习极限、微分、积 分等重要概念，为学生学习其它学科以至于专业课程打下扎实基 础。培养学生较强的动手能力，以及思维的逻辑性、严谨性、创新 性，以及利用数学原理和方法解决实际问题的意识、兴趣和能力。 培养学生掌握高等数学的基本理论和方法，尤其是思维方式，掌握 知识技能的同时发展创造能力。 Advanced mathematical modeling is the foundation of science and engineering courses. By learning the important concepts of limit, differential and integral, it can lay a solid foundation for students to learn other subjects and even professional courses. To cultivate students' strong practical ability, logical, rigorous and innovative thinking, as well as the consciousness, interest and ability of solving practical problems by using mathematical principles and methods. Cultivate students to master the basic theories and methods of higher mathematics, especially the way of thinking, master knowledge and skills, and develop creative ability at the same time. （1）专业目标: Professional Ability 1-1 具有扎实的专业基础与学科特长，系统掌握统计与数据分 析、智能仿真建模技术、量化管理优化技术、试验设计与分 析、项目管理与决策及其相关领域的专门知识与技能。 A solid professional foundation and competency, systematical mastery of the specialized knowledge and skills in statistics and data analysis, intelligent simulation modeling technology, quantitative management optimization technology, experimental design and analysis, project management and decision-making. 1-2 具有扎实的专业基础与学科特长，系统掌握信息通信系统、 项目管理与决策及其相关领域专门知识与技能。 Excellent engineering literacy, outstanding practical skills in information technology, and capable of creatively solving complex engineering problems in information and communication and related fields through scientific and technological theories and engineering practical methods, as well as the ability of doing academic cutting-edge project research. 1-3 具有扎实的专业基础与学科特长，系统掌握大数据与人工智 能系统、项目管理与决策及其相关领域专门知识与技能。 Excellent engineering literacy, outstanding practical skills in information technology, and capable of creatively solving complex engineering problems in computer science and related fields through scientific and technological theories and engineering practical methods, as well as the ability of doing academic cutting-edge project research
具有卓越的技术素养和突出的应用统计学实践能力，具备在应用统计学及其相关领域通过科学技术理论和方法创造性的解决复杂问题、从事学术前沿问题研究的能力。Excellent technical literacy, outstanding practical skills in1-4applied statistics,and capable of creatively solving complexengineering problems in applied statistics and relatedfieldsthrough scientific and technological theories and engineeringpractical methods, as well as the ability of doing academiccutting-edge project research.理解高等数学理论知识对于刻画工程实践问题的重要意义。2-1Understandthesignificant meaningsof theadvancedmathematics indepicting thepractical engineeringproblems认知当前全球，数学理论的发展对提升中国工程关键技术及（2）德育目标：核心竞争力的重要意义。Essential Quality2-2Understand the technology development, key techniques andthe core competitiveness in the area of the China engineering inthe world课程教学目标与毕业要求的对应关系MatrixofGA&SLOs毕业要求GA指标点GAIndex教学目标SLOs指标点1-1：具有较强的演绎推理能力、1、理学知识：具有扎实的数准确计算能力、分析归纳能力、抽象思学基础，能够将数学、自然维能力，掌握数学、自然科学和相关专科学和专业知识用于解决复业知识，并使用其建立正确的数学、物杂实际问题。理学等模型以解释复杂实际问题。knowledgeApplyofCapable of deductive reasoning,accurate11-1, 1-2mathematics, natural science,calculation, analysis and induction andfundamentalsandabstract thinking. Establishing correctanengineering specialization tomathematical and physical models with thethesolutionofcomplexprofessional knowledgeof mathematics,engineering problems.natural science,etc.tosolve complexpractical problems2-1能够应用数学、自然科学和工程学的基本原理、方法和手段，分析、识别、2、问题分析：能够借助应表达本专业相关的复杂工程问题。用统计学的基本原理、方法1-2, 1-3, 2-1和手段，识别、表达、并通Capableof analyzing,identifyingandelaborating complex practical problems过文献研究分析复杂实际问题，以获得有效结论。relatedtothismajorwiththeapplying ofIdentify, formulate, researchthebasicprinciplesofApplied Statisticsliteratureandanalyze2-2能够应用数学、自然科学和工程学的complex practical problems基本原理、方法和手段，针对实际复杂substantiatedreaching工程问题设计针对性的技术方案，并综conclusionsfirst合运用文献、科学基座和技术手段予以1-3, 1-4, 2-1, 2-2usingprinciples of mathematics and解决。sciences.Capableof drawingonthebasicprinciplesof applied statistics to design targeted4/15
4 / 15 1-4 具有卓越的技术素养和突出的应用统计学实践能力，具备在 应用统计学及其相关领域通过科学技术理论和方法创造性 的解决复杂问题、从事学术前沿问题研究的能力。 Excellent technical literacy, outstanding practical skills in applied statistics, and capable of creatively solving complex engineering problems in applied statistics and related fields through scientific and technological theories and engineering practical methods, as well as the ability of doing academic cutting-edge project research. （2）德育目标: Essential Quality 2-1 理解高等数学理论知识对于刻画工程实践问题的重要意义。 Understand the significant meanings of the advanced mathematics in depicting the practical engineering problems. 2-2 认知当前全球，数学理论的发展对提升中国工程关键技术及 核心竞争力的重要意义。 Understand the technology development, key techniques and the core competitiveness in the area of the China engineering in the world. 课程教学目标与毕业要求的对应关系 Matrix of GA & SLOs 毕业要求 GA 指标点 GA Index 教学目标 SLOs 1、理学知识：具有扎实的数 学基础，能够将数学、自然 科学和专业知识用于解决复 杂实际问题。 Apply knowledge of mathematics, natural science, fundamentals and an engineering specialization to the solution of complex engineering problems. 指标点 1-1：具有较强的演绎推理能力、 准确计算能力、分析归纳能力、抽象思 维能力，掌握数学、自然科学和相关专 业知识，并使用其建立正确的数学、物 理学等模型以解释复杂实际问题。 Capable of deductive reasoning, accurate calculation, analysis and induction and abstract thinking. Establishing correct mathematical and physical models with the professional knowledge of mathematics, natural science, etc. to solve complex practical problems. 1-1, 1-2 2、问题分析: 能够借助应 用统计学的基本原理、方法 和手段，识别、表达、并通 过文献研究分析复杂实际问 题，以获得有效结论。 Identify, formulate, research literature and analyze complex practical problems reaching substantiated conclusions using first principles of mathematics and sciences. 2-1 能够应用数学、自然科学和工程学的 基本原理、方法和手段，分析、识别、 表达本专业相关的复杂工程问题。 Capable of analyzing, identifying and elaborating complex practical problems related to this major with the applying of the basic principles of Applied Statistics. 1-2, 1-3, 2-1 2-2 能够应用数学、自然科学和工程学的 基本原理、方法和手段，针对实际复杂 工程问题设计针对性的技术方案，并综 合运用文献、科学基座和技术手段予以 解决。 Capable of drawing on the basic principles of applied statistics to design targeted 1-3, 1-4, 2-1, 2-2
schemesforcomplexpracticalproblems,and using literature, scientific theories andtechnical means to solve them三、教学内容Content(Topics)注：以中英文填写，各部分内容的表格可根据实际知识单元数量进行复制、扩展或缩减Note: Filled in both CN and EN, extend or reduce based on the actual numbers of knowledge unit(1)理论教学Lecture知识单元序号支撑教学目标：11-1, 1-2, 1-3, 1-4Knowledge Unit NoSLOs Supported知识单元名称微分方程及其应用Unit TitleDifferential equations and its applications-阶微分方程及其应用First OrderDifferential Equations and ItsApplications可分离变量一阶微分方程解法Solvingrules for Equationscan beReduced to Equations with知识点：Variables SeparableKnowledge Delivery高阶线性微分方程解法Solving rules for Higher Order Linear Differential Equations高阶微分方程的应用SomeExamplesof LinearDifferential Equationof HigherOrder一阶微分方程及其应用First Order Differential Equations and Its Applications了解：高阶微分方程的应用RecognizeSome Examples of Linear Differential Equation ofHigher Order学习目标可分离变量一阶微分方程解法理解：Learning ObjectivesSolving rules for Equations can be Reduced toUnderstandEquations with Variables Separable高阶线性微分方程解法掌握：Solving rules for Higher Order Linear DifferentialMasterEquations2-2认知当前全球，数学理论的发展对提升中国工程关键技术及核德育目标心竞争力的重要意义。Moral ObjectivesUnderstand thetechnologydevelopment,keytechniquesand thecorecompetitiveness in the area of the China engineering in the world可分离变量一阶微分方程解法重点：Solving rules for Equations can be Reduced to Equations withKey PointsVariables Separable难点：高阶线性微分方程解法Focal pointsSolving rules for Higher Order Linear Differential Equations5/15
5 / 15 schemes for complex practical problems, and using literature, scientific theories and technical means to solve them. 三、教学内容 Content (Topics) 注：以中英文填写，各部分内容的表格可根据实际知识单元数量进行复制、扩展或缩减 Note: Filled in both CN and EN, extend or reduce based on the actual numbers of knowledge unit (1) 理论教学 Lecture 知识单元序号: Knowledge Unit No. 1 支撑教学目标: SLOs Supported 1-1，1-2，1-3，1-4 知识单元名称 Unit Title 微分方程及其应用 Differential equations and its applications 知识点: Knowledge Delivery 一阶微分方程及其应用 First Order Differential Equations and Its Applications 可分离变量一阶微分方程解法 Solving rules for Equations can be Reduced to Equations with Variables Separable 高阶线性微分方程解法 Solving rules for Higher Order Linear Differential Equations 高阶微分方程的应用 Some Examples of Linear Differential Equation of Higher Order 学习目标: Learning Objectives 了解: Recognize 一阶微分方程及其应用 First Order Differential Equations and Its Applications 高阶微分方程的应用 Some Examples of Linear Differential Equation of Higher Order 理解: Understand 可分离变量一阶微分方程解法 Solving rules for Equations can be Reduced to Equations with Variables Separable 掌握: Master 高阶线性微分方程解法 Solving rules for Higher Order Linear Differential Equations 德育目标 Moral Objectives 2-2 认知当前全球，数学理论的发展对提升中国工程关键技术及核 心竞争力的重要意义。 Understand the technology development, key techniques and the core competitiveness in the area of the China engineering in the world. 重点: Key Points 可分离变量一阶微分方程解法 Solving rules for Equations can be Reduced to Equations with Variables Separable 难点: Focal points 高阶线性微分方程解法 Solving rules for Higher Order Linear Differential Equations
知识单元序号支撑教学目标：21-1, 1-2, 1-3, 1-4Knowledge Unit No.SLOs Supported知识单元名称级数及其应用Unit TitleSeries and its applications常数级数的概念与性质Concepts and properties of Series with Constant Terms常数级数的收敛判据知识点：Convergencecriteriafor Series with Constant TermsKnowledge Delivery幂级数及其收敛性Power Series and Their Convergence幂级数的展开Expansion of Functions in Power Series了解：常数级数的概念与性质RecognizeConcepts and properties of Series with Constant Terms理解：常数级数的收敛判据学习目标：UnderstandConvergencecriteriafor Series with Constant TermsLearning Objectives幂级数及其收敛性掌握：Power Series and TheirConvergenceMaster幂级数的展开Expansion of Functions inPower Series2-2认知当前全球，数学理论的发展对提升中国工程关键技术及核德育目标心竞争力的重要意义。Moral ObjectivesUnderstand the technology development, key techniques and the corecompetitiveness in the area of the China engineering in the world重点：常数级数的收敛判据Key PointsConvergence criteria for Series with Constant Terms幂级数及其收敛性难点：Power Series and Their ConvergenceFocal points幂级数的展开Expansion of FunctionsinPower Series知识单元序号支撑教学目标：31-1,1-2, 1-3,1-4Knowledge Unit No.SLOs Supported向量与解析几何知识单元名称Unit TitleVectors and Analytic Geometry平面与空间的向量Vectors in plane and surface向量的积知识点：Product of vectorKnowledge Delivery空间中的平面与直线Planes and lines in plane平面与空间曲线Surfaces and Space Curves学习目标：了解：平面与空间的向量Learning ObjectivesRecognizeVectors in plane and surface6/15
6 / 15 知识单元序号: Knowledge Unit No. 2 支撑教学目标: SLOs Supported 1-1，1-2，1-3，1-4 知识单元名称 Unit Title 级数及其应用 Series and its applications 知识点: Knowledge Delivery 常数级数的概念与性质 Concepts and properties of Series with Constant Terms 常数级数的收敛判据 Convergence criteria for Series with Constant Terms 幂级数及其收敛性 Power Series and Their Convergence 幂级数的展开 Expansion of Functions in Power Series 学习目标: Learning Objectives 了解: Recognize 常数级数的概念与性质 Concepts and properties of Series with Constant Terms 理解: Understand 常数级数的收敛判据 Convergence criteria for Series with Constant Terms 掌握: Master 幂级数及其收敛性 Power Series and Their Convergence 幂级数的展开 Expansion of Functions in Power Series 德育目标 Moral Objectives 2-2 认知当前全球，数学理论的发展对提升中国工程关键技术及核 心竞争力的重要意义。 Understand the technology development, key techniques and the core competitiveness in the area of the China engineering in the world. 重点: Key Points 常数级数的收敛判据 Convergence criteria for Series with Constant Terms 难点: Focal points 幂级数及其收敛性 Power Series and Their Convergence 幂级数的展开 Expansion of Functions in Power Series 知识单元序号: Knowledge Unit No. 3 支撑教学目标: SLOs Supported 1-1，1-2，1-3，1-4 知识单元名称 Unit Title 向量与解析几何 Vectors and Analytic Geometry 知识点: Knowledge Delivery 平面与空间的向量 Vectors in plane and surface 向量的积 Product of vector 空间中的平面与直线 Planes and lines in plane 平面与空间曲线 Surfaces and Space Curves 学习目标: Learning Objectives 了解: Recognize 平面与空间的向量 Vectors in plane and surface
向量的积Product of vector空间中的平面与直线理解：Planesand linesinplaneUnderstand平面与空间曲线Surfaces and Space Curves空间中的平面与直线的求法与性质掌握：Propertiesand evaluation of planes and lines in planeMaster平面与空间曲线的求法与性质Propertiesandevaluationof surfacesand SpaceCurves2-2认知当前全球，数学理论的发展对提升中国工程关键技术及核德育目标心竞争力的重要意义。Moral ObjectivesUnderstand the technology development,key techniques and the corecompetitiveness in the area of the China engineering in the world.重点：空间中的平面与直线的求法与性质Key PointsProperties and evaluation ofplanes and lines in plane难点：平面与空间曲线的求法与性质Focal pointsProperties andevaluation ofsurfaces and SpaceCurves支撑教学目标知识单元序号：41-1, 1-2, 1-3, 1-4Knowledge Unit No.SLOs Supported知识单元名称多元函数及其分析性质Unit TitleMultiplevariables function and its analyticproperties多变量函数，n维空间的定义以及其性质；Definitionofandpropertiesofmulti-variablefunctionandn-dimensional space.二元函数极限的定义与性质以及二元函数连续性的定义与性质Thedefinition and properties of two-variablefunction多元函数的偏导数与全微分的概念与应用Thedefinition and application of partial derivative of multiple-variablefunction知识点多元复合函数的偏导数求法Knowledge DeliveryThepartial derivationruleofmultiple-variablecompositefunction由方程组确定的隐函数求偏导方法Derivation method of findingpartial derivative of implicit functionsdetermined by equation systems.多元函数的几何应用Applicationsofmultiple-variablefunctionsinGeometry多元函数的极值Extreme values of multiple-variable functions学习目标：了解：多变量函数及性质；Learning ObjectivesRecognizeProperties of multi-variable function7/15
7 / 15 向量的积 Product of vector 理解: Understand 空间中的平面与直线 Planes and lines in plane 平面与空间曲线 Surfaces and Space Curves 掌握: Master 空间中的平面与直线的求法与性质 Properties and evaluation of planes and lines in plane 平面与空间曲线的求法与性质 Properties and evaluation of surfaces and Space Curves 德育目标 Moral Objectives 2-2 认知当前全球，数学理论的发展对提升中国工程关键技术及核 心竞争力的重要意义。 Understand the technology development, key techniques and the core competitiveness in the area of the China engineering in the world. 重点: Key Points 空间中的平面与直线的求法与性质 Properties and evaluation of planes and lines in plane 难点: Focal points 平面与空间曲线的求法与性质 Properties and evaluation of surfaces and Space Curves 知识单元序号: Knowledge Unit No. 4 支撑教学目标: SLOs Supported 1-1，1-2，1-3，1-4 知识单元名称 Unit Title 多元函数及其分析性质 Multiple variables function and its analytic properties 知识点: Knowledge Delivery 多变量函数, n 维空间的定义以及其性质； Definition of and properties of multi-variable function and n-dimensional space. 二元函数极限的定义与性质以及二元函数连续性的定义与性质 The definition and properties of two-variable function. 多元函数的偏导数与全微分的概念与应用 The definition and application of partial derivative of multiple-variable function 多元复合函数的偏导数求法 The partial derivation rule of multiple-variable composite function 由方程组确定的隐函数求偏导方法 Derivation method of finding partial derivative of implicit functions determined by equation systems. 多元函数的几何应用 Applications of multiple-variable functions in Geometry 多元函数的极值 Extreme values of multiple-variable functions 学习目标: Learning Objectives 了解: Recognize 多变量函数及性质； Properties of multi-variable function
二元连续函数在闭区域上的性质The properties of two-variable function on a closedregion多元函数全微分的概念与应用Definition and utilization of total differentialof理解：multiple-variablefunctionUnderstand高阶偏导数的概念与应用Definition and utilization of higher order partialderivative多元复合函数求偏导的链式法则Chainruleof findingpartialderivativeof掌握：multiple-variablecompositefunctionMaster拉格朗日函数构造方法Formulation method of Lagrange multipliers findingextreme values.2-1理解高等数学理论知识对于刻画工程实践问题的重要意义。德育目标Understand the significant meanings of the advanced mathematics inMoral Objectivesdepicting thepractical engineeringproblems多元函数全微分的概念与应用Definition and utilization of total differential of multiple-variable重点：functionKey Points高阶偏导数的概念与应用Definition and utilization of higher order partial derivative多元复合函数求偏导的链式法则Chainrule of findingpartial derivative ofmultiple-variable composite难点：functionFocal points拉格朗日函数构造方法Formulationmethod of Lagrangemultipliersfindingextremevalues支撑教学目标：知识单元序号：51-1, 1-2, 1-3, 1-4Knowledge Unit No.SLOs Supported知识单元名称多重积分及其分析性质Unit TitleMultiple Integral and its analytic properties二重积分的概念与性质Definition and propertiesofdouble integrals求解二重积分的方法知识点：Evaluation of double integralsKnowledge Delivery三重积分的概念与性质Definition and propertiesof triple integrals求解三重积分的方法Evaluation of triple integrals二重积分的几何意义了解：学习目标Geometricmeaningofdouble integrals三重积分的几何意义Learning ObjectivesRecognizeGeometricmeaningoftripleintegrals8/15
8 / 15 二元连续函数在闭区域上的性质 The properties of two-variable function on a closed region 理解: Understand 多元函数全微分的概念与应用 Definition and utilization of total differential of multiple-variable function 高阶偏导数的概念与应用 Definition and utilization of higher order partial derivative 掌握: Master 多元复合函数求偏导的链式法则 Chain rule of finding partial derivative of multiple-variable composite function 拉格朗日函数构造方法 Formulation method of Lagrange multipliers finding extreme values. 德育目标 Moral Objectives 2-1 理解高等数学理论知识对于刻画工程实践问题的重要意义。 Understand the significant meanings of the advanced mathematics in depicting the practical engineering problems. 重点: Key Points 多元函数全微分的概念与应用 Definition and utilization of total differential of multiple-variable function 高阶偏导数的概念与应用 Definition and utilization of higher order partial derivative 难点: Focal points 多元复合函数求偏导的链式法则 Chain rule of finding partial derivative of multiple-variable composite function 拉格朗日函数构造方法 Formulation method of Lagrange multipliers finding extreme values. 知识单元序号: Knowledge Unit No. 5 支撑教学目标: SLOs Supported 1-1，1-2，1-3，1-4 知识单元名称 Unit Title 多重积分及其分析性质 Multiple Integral and its analytic properties 知识点: Knowledge Delivery 二重积分的概念与性质 Definition and properties of double integrals 求解二重积分的方法 Evaluation of double integrals 三重积分的概念与性质 Definition and properties of triple integrals 求解三重积分的方法 Evaluation of triple integrals 学习目标: Learning Objectives 了解: Recognize 二重积分的几何意义 Geometric meaning of double integrals 三重积分的几何意义 Geometric meaning of triple integrals
直角坐标系下二重积分求法理解：Double integrals in rectangular coordinatesUnderstand极坐标系下二重积分求法Double integrals in polar coordinates二重、三重积分的性质Properties of doubleand triple integrals掌握：直角坐标系下三重积分求法MasterTriple integrals in rectangular coordinates球坐标系下三重积分求法Triple integrals in spherical coordinates2-1理解高等数学理论知识对于刻画工程实践问题的重要意义。德育目标Understand the significant meanings of theadvanced mathematics inMoral Objectivesdepictingthepracticalengineeringproblems重点：直角坐标系下三重积分求法Key PointsTriple integrals in rectangular coordinates难点：球坐标系下三重积分求法Focal pointsTriple integrals in spherical coordinates知识单元序号：支撑教学目标61-1, 1-2, 1-3, 1-4Knowledge Unit No.SLOs Supported知识单元名称线积分、面积分Unit TitleLine Integrals, Surface Integrals线积分的概念与性质Definition and properties of line integrals求解线积分的方法知识点：Evaluation of line integralsKnowledge Delivery面积分的概念与性质Definition and properties of surface integrals求解面积分的方法Evaluation of surface integrals线积分的几何意义了解：Geometricmeaning of line integrals三重积分的几何意义RecognizeGeometricmeaning ofsurface integrals理解：格林公式、斯托克斯公式学习目标：UnderstandGreen's Formula, Stokes' Formula线积分与路径无关性质Learning ObjectivesPropertiesofpathindependenceof lineintegral掌握：求解线积分的方法MasterEvaluation of line integrals面积分的概念与性质Definitionandpropertiesofsurface integrals2-1理解高等数学理论知识对于刻画工程实践问题的重要意义。德育目标Understand the significant meanings of the advanced mathematics inMoral Objectivesdepictingthepractical engineeringproblems9/15
9 / 15 理解: Understand 直角坐标系下二重积分求法 Double integrals in rectangular coordinates 极坐标系下二重积分求法 Double integrals in polar coordinates 掌握: Master 二重、三重积分的性质 Properties of double and triple integrals 直角坐标系下三重积分求法 Triple integrals in rectangular coordinates 球坐标系下三重积分求法 Triple integrals in spherical coordinates 德育目标 Moral Objectives 2-1 理解高等数学理论知识对于刻画工程实践问题的重要意义。 Understand the significant meanings of the advanced mathematics in depicting the practical engineering problems. 重点: Key Points 直角坐标系下三重积分求法 Triple integrals in rectangular coordinates 难点: Focal points 球坐标系下三重积分求法 Triple integrals in spherical coordinates 知识单元序号: Knowledge Unit No. 6 支撑教学目标: SLOs Supported 1-1，1-2，1-3，1-4 知识单元名称 Unit Title 线积分、面积分 Line Integrals, Surface Integrals 知识点: Knowledge Delivery 线积分的概念与性质 Definition and properties of line integrals 求解线积分的方法 Evaluation of line integrals 面积分的概念与性质 Definition and properties of surface integrals 求解面积分的方法 Evaluation of surface integrals 学习目标: Learning Objectives 了解: Recognize 线积分的几何意义 Geometric meaning of line integrals 三重积分的几何意义 Geometric meaning of surface integrals 理解: Understand 格林公式、斯托克斯公式 Green’s Formula, Stokes’ Formula 掌握: Master 线积分与路径无关性质 Properties of path independence of line integral 求解线积分的方法 Evaluation of line integrals 面积分的概念与性质 Definition and properties of surface integrals 德育目标 Moral Objectives 2-1 理解高等数学理论知识对于刻画工程实践问题的重要意义。 Understand the significant meanings of the advanced mathematics in depicting the practical engineering problems
重点：格林公式、斯托克斯公式Key PointsGreen'sFormula,Stokes'Formula难点：线积分与路径无关性质Focal pointsPropertiesof pathindependenceof line integral知识单元序号支撑教学目标：11-1, 1-2, 1-3, 1-4Knowledge Unit No.SLOs Supported统计学概念及性质知识单元名称Unit TitleDefinitions of Statistics and its properties描述性统计学概述：Overviewand descriptivestatistics样本空间、事件，概率的公理化定义、解释和性质、概率的计算；知识点：Sample spaces and events, axioms, interpretations, and properties ofKnowledge Deliveryprobability,countingtechniques条件概率，事件的独立：Conditional probability,independence了解：统计学基本概念；RecognizeBasicconcepts in statistics理解：概率的性质、计算；学习目标：UnderstandPropertiesofprobabilityand countingtechniquesLearning Objectives全概率公式，贝叶斯定理，事件的独立；掌握：theLawoftotalprobability,Bayes'theorem,Masterindependence2-2认知当前全球，数学理论的发展对提升中国工程关键技术及核德育目标心竞争力的重要意义。Moral ObjectivesUnderstand thetechnology development,keytechnigues and the corecompetitiveness in the area of the China engineering in the world重点：概率的性质、计算；Key PointsProperties of probabilityand counting techniques难点：全概率公式，贝叶斯定理，事件的独立；Focal pointstheLawoftotalprobability，Bayestheorem,independence知识单元序号支撑教学目标：91-1, 1-2, 1-3, 1-4Knowledge Unit NoSLOs Supported知识单元名称随机变量以及概率分布Unit TitleRandomvariableandprobabilitydistribution随机变量、离散性随机变量的分布以及期望；Randomvariables,probabilitydistributions fordiscreterandomvariables, expected values知识点二项分布及泊松分布；Knowledge DeliveryThe binomial probability distribution and the Poisson probabilitydistribution概率密度函数，分布函数和期望；Probability density functions, cumulative distribution functions and10 /15
10 / 15 重点: Key Points 格林公式、斯托克斯公式 Green’s Formula, Stokes’ Formula 难点: Focal points 线积分与路径无关性质 Properties of path independence of line integral 知识单元序号: Knowledge Unit No. 7 支撑教学目标: SLOs Supported 1-1，1-2，1-3，1-4 知识单元名称 Unit Title 统计学概念及性质 Definitions of Statistics and its properties 知识点: Knowledge Delivery 描述性统计学概述； Overview and descriptive statistics 样本空间、事件，概率的公理化定义、解释和性质、概率的计算； Sample spaces and events, axioms, interpretations, and properties of probability, counting techniques 条件概率，事件的独立； Conditional probability, independence 学习目标: Learning Objectives 了解: Recognize 统计学基本概念； Basicconcepts in statistics 理解: Understand 概率的性质、计算； Properties of probability and counting techniques 掌握: Master 全概率公式，贝叶斯定理，事件的独立； the Law of total probability， Bayes’ theorem, independence 德育目标 Moral Objectives 2-2 认知当前全球，数学理论的发展对提升中国工程关键技术及核 心竞争力的重要意义。 Understand the technology development, key techniques and the core competitiveness in the area of the China engineering in the world. 重点: Key Points 概率的性质、计算； Properties of probability and counting techniques 难点: Focal points 全概率公式，贝叶斯定理，事件的独立； the Law of total probability， Bayes’ theorem, independence 知识单元序号: Knowledge Unit No. 8 支撑教学目标: SLOs Supported 1-1，1-2，1-3，1-4 知识单元名称 Unit Title 随机变量以及概率分布 Random variable and probability distribution 知识点: Knowledge Delivery 随机变量、离散性随机变量的分布以及期望； Random variables, probability distributions for discrete random variables, expected values 二项分布及泊松分布； The binomial probability distribution and the Poisson probability distribution 概率密度函数，分布函数和期望； Probability density functions, cumulative distribution functions and