数学分析与建模（二）教学大纲MathematicalAnalysis and)SubjectSyllabusModeling(II)，课程信息SubjectInformation课程编号：开课学期：23100311002Subject IDSemester课程分类：所属课群：专业教育PA专业基础MFCategorySection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 Smart应用统计学ASCollegeTechnologyCollegeStreamNortheastemUniversity课程属性：课程模式：必修Compulsory互认EQVPatternMode中方课程协调人王晓敏成绩记载方式：百分制MarksNEU CoordinatorWangXiaominResult Type先修课程：数学分析与建模（一）MathematicalAnalysisandModeling(I)RequisitesMoHuixia,LiXiaohua,Yuan Jianhua,Yuan Jianhua,Ai Wenbao,Zhu英文参考教材Ping,AdvancedMathematics(Il),2ndEdition,BeijingUniversity ofENTextbooksPostsandTelecommunicationsPress,2018邓东皋，尹小玲，数学分析简明教程（第二版）下册，高等教育出版中文参考教材：社,2006.CN Textbooks同济大学数学系，高等数学（第七版）下册，高等教育出版社.2015教学资源：https://sstc.cloudcampus.com.cn/course/view.php?id=gResources王晓敏提交日期：课程负责人(撰写人)：3/3/2023Subject DirectorWangXiaominSubmitted Date任课教师(含负责人)：王晓敏、刘艳杰Taught byWang Xiaomin, Liu Yanjie审核人：批准人：韩鹏史闻博Checked byApproved by批准日期：3/6/2023Approved Date1/ 12
1 / 12 数学分析与建模（二） 教学大纲 Subject Syllabus Mathematical Analysis and Modeling(II) 一、课程信息 Subject Information 课程编号: Subject ID 3100311002 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 应用统计学 AS 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 王晓敏 Wang Xiaomin 成绩记载方式: Result Type 百分制 Marks 先修课程: Requisites 数学分析与建模（一）Mathematical Analysis and Modeling (I) 英文参考教材: EN Textbooks Mo Huixia, Li Xiaohua, Yuan Jianhua, Yuan Jianhua, Ai Wenbao, Zhu Ping, Advanced Mathematics (II), 2nd Edition, Beijing University of Posts and Telecommunications Press, 2018. 中文参考教材: CN Textbooks 邓东皋，尹小玲，数学分析简明教程(第二版) 下册，高等教育出版 社, 2006. 同济大学数学系, 高等数学(第七版)下册, 高等教育出版社, 2015. 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 王晓敏 Wang Xiaomin 提交日期: Submitted Date 3/3/2023 任课教师(含负责人): Taught by 王晓敏、刘艳杰 Wang Xiaomin, Liu Yanjie 审核人: Checked by 韩鹏 批准人: Approved by 史闻博 批准日期: Approved Date 3/6/2023
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:GAand indexcan bereferredfrom undergraduate program in SSTCwebsite.Please add/reduce lines basedon subject数学分析与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。整体目标：Mathematical analysis and modeling is the foundation of science andOverallengineering courses. By learning the important concepts of limit, differentialObjectiveand integral, it can lay a solid foundation for students to learn other subjectsand even professional courses. To cultivate students' strong practical ability.logical,rigorous and innovative thinking,as well as the consciousness,interestand ability of solving practical problems by using mathematical principles andmethods.Cultivate students tomaster thebasic theories and methods of highermathematics,especiallythewayofthinking,masterknowledgeand skills,anddevelop creativeability 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 solidprofessional foundation and competency,systematical1-1mastery of the specialized knowledge and skills in statistics and dataanalysis, intelligent simulation modeling technology, quantitativemanagement optimization technology,experimental design andanalysis, project management and decision-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 skills ininformation technology, and capable of creatively solving complex1-2(1)专业目标：engineering problems in information and communication and relatedProfessionalfields through scientific and technological theories and engineeringAbilitypractical methods, as well as the ability of doing academiccutting-edge project research.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 solving complex1-3 engineering problems in computer science and related fields throughscientific and technological theories and engineering practicalmethods, as well as the ability of doing academic cutting-edgeproject 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1-4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。2 /12
2 / 12 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 数学分析与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。 Mathematical analysis and 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. 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 appliedstatistics, and capable of creatively solving complex engineeringproblems in applied statistics and related fields through scientific andtechnological theories and engineering practical methods, as well asthe ability of doing academic cutting-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。2-1Understand the significant meanings of the advanced mathematics indepictingthepracticalengineeringproblems(2)德育目标：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Essential竞争力的重要意义。Quality2-2Understand the technology development, key techniques and the corecompetitiveness 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MatrixofGA&SLOs毕业要求GA指标点GAIndex教学目标SLOs1、理学知识：具有扎指标点1-1：具有较强的演绎推理能力、准确实的数学基础，能够将计算能力、分析归纳能力、抽象思维能力，掌数学、自然科学和专业握数学、自然科学和相关专业知识，并使用其知识用于解决复杂实建立正确的数学、物理学等模型以解释复杂实际问题。际问题。Applyknowledgeof1-1, 1-2Capableofdeductivereasoning,accuratemathematics,naturalcalculation,analysis and induction and abstractscience, fundamentalsthinking.Establishing correctmathematical andand an engineeringphysicalmodelswiththeprofessionalspecialization to theknowledgeof mathematics, natural science, etcsolution of complextosolvecomplexpracticalproblemsengineering problems2-1能够应用数学、自然科学和工程学的基本2、问题分析：能够借原理、方法和手段，分析、识别、表达本专业助应用统计学的基本相关的复杂工程问题。原理、方法和手段，识identifying1-2, 1-3, 2-1Capableofanalyzing，and别、表达、并通过文献elaborating complex practical problems related研究分析复杂实际问to this major with the applying of the basic题，以获得有效结论。principlesofApplied StatisticsIdentify,formulate,2-2能够应用数学、自然科学和工程学的基本research literature and原理、方法和手段，针对实际复杂工程问题设analyzecomplex计针对性的技术方案，并综合运用文献、科学problemspractical基座和技术手段予以解决。reachingsubstantiated1-3, 1-4, 2-1, 2-2Capable of drawing on the basic principles ofconclusions using firstapplied statistics to design targeted schemes forprinciplesofcomplex practical problems, and using literature,mathematicsandscientific theories and technical means to solvesciencesthem.3/12
3 / 12 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 schemes for complex practical problems, and using literature, scientific theories and technical means to solve them. 1-3, 1-4, 2-1, 2-2
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 No.SLOs Supported实数连续性知识单元名称Unit TitleContinuity of Real Numbers实数连续性的等价描述Equivalentdescriptionofcontinuityof real numbers实数闭区间的致密性Compactness of closed intervals of real numbers知识点：实数的完备性Knowledge DeliveryCompletenessof realnumbers闭区间上连续函数的性质Properties ofcontinuousfunctionson closed intervals实数集的上确界、下确界、覆盖的概念了解：Concepts of supremum,infimumand cover of realRecognizenumbersets确界原理、单调有界原理、有限覆盖定理、区间套定理、致密性定理、柯西收敛原理的相互等价性理解：The mutual equivalence of supremum and infimumUnderstandprinciple, monotone bounded principle, finite covering学习目标theorem, nested interval theorem,compactness theoremLearning Objectivesand Cauchy convergence principle上述定理相互等价的证明思路和方法Ideasand methodsforprovingthe equivalenceof the掌握：abovetheoremsMaster闭区间上连续函数的性质的证明思路和方法Ideasandmethodsforprovingthepropertiesofcontinuous functions on closed intervals2-2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确界定理、单调有界原理、有限覆盖定理重点：supremumand infimumtheorem,monotoneboundedprinciple,finiteKey Pointscovering theorem难点：上述定理相互等价的证明思路和方法Focal pointsIdeas and methodsforproving the equivalenceofthe abovetheorems4/12
4 / 12 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 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 实数连续性 Continuity of Real Numbers 知识点: Knowledge Delivery 实数连续性的等价描述 Equivalent description of continuity of real numbers 实数闭区间的致密性 Compactness of closed intervals of real numbers 实数的完备性 Completeness of real numbers 闭区间上连续函数的性质 Properties of continuous functions on closed intervals 学习目标: Learning Objectives 了解: Recognize 实数集的上确界、下确界、覆盖的概念 Concepts of supremum, infimum and cover of real number sets 理解: Understand 确界原理、单调有界原理、有限覆盖定理、区间套定 理、致密性定理、柯西收敛原理的相互等价性 The mutual equivalence of supremum and infimum principle, monotone bounded principle, finite covering theorem, nested interval theorem, compactness theorem and Cauchy convergence principle 掌握: Master 上述定理相互等价的证明思路和方法 Ideas and methods for proving the equivalence of the above theorems 闭区间上连续函数的性质的证明思路和方法 Ideas and methods for proving the properties of continuous functions on closed intervals 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 确界定理、单调有界原理、有限覆盖定理 supremum and infimum theorem, monotone bounded principle, finite covering theorem 难点: Focal points 上述定理相互等价的证明思路和方法 Ideas and methods for proving the equivalence of the above theorems
知识单元序号支撑教学目标：21-1,1-2,1-3,1-4Knowledge UnitNoSLOs Supported知识单元名称数项级数Unit TitleSeries with Constant Terms数项级数的收敛与发散Convergence and divergence ofa series with constant terms级数的性质Propertiesofseries数项级数收敛的必要条件知识点：Anecessary conditionforconvergenceofa serieswithconstanttermsKnowledge Delivery正项级数收敛性的判别法Convergencetests for series withpositiveterms柯西收敛原理Cauchyconvergenceprinciple般项级数的收敛性判别法General series and tests for convergence数项级数收敛、发散以及收敛级数的和的概念了解：Concept of convergence, divergence of series and theRecognizesum of convergent series级数的性质Propertiesofseries狄利克雷判别法和阿贝尔判别法理解：学习目标Dirichlet test and Abel test无穷级数与广义积分之间的共同点与差异Learning ObjectivesUnderstandSimilarities and differences between infinite series andgeneralized integral正项级数收敛性的判别法掌握：Convergence tests for series with positivetermsMaster莱布尼茨判别法Leibniztest2-1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 engineeringproblems正项级数收敛性的判别法重点：ConvergenceTestsfor Series withPositiveTermsKey Points莱布尼茨判别法Leibniztest难点：柯西收敛原理CauchyconvergenceprincipleFocal points知识单元序号支撑教学目标31-1,1-2,1-3,1-4Knowledge Unit No.SLOs Supported函数项级数知识单元名称Unit TitleFunctional Series函数项级数的收敛域与和函数Convergence domain and sum function of functional series知识点：函数项级数的一致收敛的概念Knowledge DeliveryConcept of uniform convergence of functional series致收敛函数项级数的性质Properties of uniformly convergent functional series5/12
5 / 12 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 数项级数 Series with Constant Terms 知识点: Knowledge Delivery 数项级数的收敛与发散 Convergence and divergence of a series with constant terms 级数的性质 Properties of series 数项级数收敛的必要条件 A necessary condition for convergence of a series with constant terms 正项级数收敛性的判别法 Convergence tests for series with positive terms 柯西收敛原理 Cauchy convergence principle 一般项级数的收敛性判别法 General series and tests for convergence 学习目标: Learning Objectives 了解: Recognize 数项级数收敛、发散以及收敛级数的和的概念 Concept of convergence, divergence of series and the sum of convergent series 理解: Understand 级数的性质 Properties of series 狄利克雷判别法和阿贝尔判别法 Dirichlet test and Abel test 无穷级数与广义积分之间的共同点与差异 Similarities and differences between infinite series and generalized integral 掌握: Master 正项级数收敛性的判别法 Convergence tests for series with positive terms 莱布尼茨判别法 Leibniz test 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 正项级数收敛性的判别法 Convergence Tests for Series with Positive Terms 莱布尼茨判别法 Leibniz test 难点: Focal points 柯西收敛原理 Cauchy convergence principle 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 函数项级数 Functional Series 知识点: Knowledge Delivery 函数项级数的收敛域与和函数 Convergence domain and sum function of functional series 函数项级数的一致收敛的概念 Concept of uniform convergence of functional series 一致收敛函数项级数的性质 Properties of uniformly convergent functional series