东北大学：某学院应用统计学专业《数学分析与建模》课程教学大纲（一）

数学分析与建模（一）教学大纲MathematicalAnalysisand)SubjectSyllabusModeling ()，课程信息SubjectInformation课程编号：开课学期：13100311001Subject IDSemester课程分类：所属课群：专业教育PA专业基础MFCategorySection总学时/周：课程学分：580/14Credit PointsTotal Hours/Weeks理论学时：实验学时：800LECT. 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开课学院适用专业：Sydney Smart应用统计学 ASCollegeTechnology CollegeStreamNortheastemUniversity课程属性：课程模式：必修Compulsory互认EQVPatternMode王晓敏成绩记载方式：中方课程协调人：百分制MarksNEU CoordinatorWangXiaominResult Type先修课程：无NoneRequisitesMoHuixia,LiXiaohua,Yuan Jianhua,Yuan Jianhua,Ai Wenbao,Zhu英文参考教材Ping,AdvancedMathematics (I),2nd Edition,Beijing University ofENTextbooksPostsandTelecommunicationsPress,2018同济大学数学系，高等数学（第七版）上册，高等教育出版社，2014中文参考教材：邓东皋，尹小玲，数学分析简明教程（第二版）上册，高等教育出版CN Textbooks社,2006教学资源：https://sstc.cloudcampus.com.cn/course/view.php?id=9Resources王晓敏课程负责人(撰写人)：提交日期：单击或点击此处输Subject DirectorSubmitted Date入日期。WangXiaomin王晓敏、刘艳杰任课教师(含负责人)：Taught byWang Xiaomin, Liu Yanjie审核人：批准人：韩鹏史闻博Checked byApproved by批准日期：单击或点击此处输入日期。Approved Date1/9

1 / 9 数学分析与建模（一） 教学大纲 Subject Syllabus Mathematical Analysis and Modeling (I) 一、课程信息 Subject Information 课程编号: Subject ID 3100311001 开课学期: Semester 1 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 5 总学时/周: Total Hours/Weeks 80/14 理论学时: LECT. Hours 80 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 无 None 英文参考教材: EN Textbooks Mo Huixia, Li Xiaohua, Yuan Jianhua, Yuan Jianhua, Ai Wenbao, Zhu Ping, Advanced Mathematics (I), 2nd Edition, Beijing University of Posts and Telecommunications Press, 2018. 中文参考教材: CN Textbooks 同济大学数学系, 高等数学(第七版)上册, 高等教育出版社, 2014. 邓东皋，尹小玲，数学分析简明教程(第二版) 上册，高等教育出版 社, 2006. 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 单击或点击此处输 入日期。 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 单击或点击此处输 入日期

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 andmodeling is thefoundation of science and整体目标：engineering courses. By learning the important concepts of limit,Overall Objectivedifferential 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 ofhighemathematics,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,quantitativemanagementoptimizationtechnology,experimental 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 research2/9

2 / 9 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

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 targeted3/9

3 / 9 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知识单元名称函数与极限Unit TitleFunctions and Limits映射与函数Mappings andfunctions数列极限Limitsofsequences知识点函数极限LimitsoffunctionsKnowledge Delivery无穷小与无穷大Infinitesimalandinfinite连续函数Continuous functions函数和初等函数的概念了解：ConceptsoffunctionsandelementaryfunctionsRecognize函数的性质Propertiesoffunctions数列和函数极限的定义理解：Definitions of limitofasequenceandafunction学习目标Understand连续函数的定义和性质Learning ObjectivesDefinition and properties of continuous functions极限的性质及运算法则掌握：Properties and operation rules of limitsMaster两个重要极限Twoimportantlimits无穷小的比较Orderoftheinfinitesimals2-2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：极限的性质及运算法则Key PointsProperties and operation rules of limits难点：极限的性质PropertiesoflimitsFocal points两个重要极限Twoimportantlimits知识单元序号支撑教学目标21-1, 1-2, 1-3, 1-4Knowledge Unit No.SLOs Supported知识单元名称导数与微分Unit TitleDerivative and Differential导数的概念Concepts ofderivatives知识点：求导法则RulesoffindingderivativesKnowledge Delivery高阶导数Higherorderderivatives4/9

4 / 9 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 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 函数与极限 Functions and Limits 知识点: Knowledge Delivery 映射与函数 Mappings and functions 数列极限 Limits of sequences 函数极限 Limits of functions 无穷小与无穷大 Infinitesimal and infinite 连续函数 Continuous functions 学习目标: Learning Objectives 了解: Recognize 函数和初等函数的概念 Concepts of functions and elementary functions 函数的性质 Properties of functions 理解: Understand 数列和函数极限的定义 Definitions of limit of a sequence and a function 连续函数的定义和性质 Definition and properties of continuous functions 掌握: Master 极限的性质及运算法则 Properties and operation rules of limits 两个重要极限 Two important limits 无穷小的比较 Order of the infinitesimals 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 极限的性质及运算法则 Properties and operation rules of limits 难点: Focal points 极限的性质 Properties of limits 两个重要极限 Two important limits 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 导数与微分 Derivative and Differential 知识点: Knowledge Delivery 导数的概念 Concepts of derivatives 求导法则 Rules of finding derivatives 高阶导数 Higher order derivatives

隐函数以及参数方程的求导数法则Derivation of implicit functions and parametric equations函数的微分Differentialofafunction了解：导数的概念ConceptofderivativesRecognize函数的微分Differentialofafunction隐函数和由参数方程所确定的函数的导数学习目标：理解：Derivationof implicit functions andparametricLearning ObjectivesUnderstandequations掌握：求导法则Rules offindingderivativesMaster高阶导数Higherorderderivatives2-1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 significantmeanings of the advanced mathematics inMoral Objectivesdepicting the practical engineering problems重点：求导法则Rules offindingderivativesKey Points高阶导数Higherorderderivatives难点：隐函数和由参数方程所确定的函数的导数Focal pointsDerivation of implicit functions and parametric equations知识单元序号支撑教学目标31-1, 1-2, 1-3, 1-4Knowledge Unit No.SLOs Supported微分中值定理与导数的应用知识单元名称Unit TitleMeanValueTheoremandApplications of Derivatives区间套定理Theoremofnestedinterval闭区间上连续函数的性质Properties of continuous functions on a closed interval知识点：微分中值定理Differentialmeanvaluetheorems洛必达法则LHospital'srulesKnowledge Delivery泰勒公式Taylor'stheorem函数单调性、极值以及凹凸性质Monotonicity,extremevalues and convexityoffunction区间套定理Theoremofnestedinterval了解：闭区间上连续函数的性质RecognizeProperties of continuous functions on a closed interval理解：微分中值定理及其证明学习目标UnderstandDifferentialmeanvaluetheoremandtheirproofsLearning Objectives罗必达法则LHospital'srules掌握：函数单调性、极值以及凹凸性质MasterMonotonicity,extremevaluesandconvexityoffunctions2-2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：拉格朗日定理Lagrange's theoremKey Points5/9

5 / 9 隐函数以及参数方程的求导数法则 Derivation of implicit functions and parametric equations 函数的微分 Differential of a function 学习目标: Learning Objectives 了解: Recognize 导数的概念 Concept of derivatives 函数的微分 Differential of a function 理解: Understand 隐函数和由参数方程所确定的函数的导数 Derivation of implicit functions and parametric equations 掌握: Master 求导法则 Rules of finding derivatives 高阶导数 Higher order derivatives 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 求导法则 Rules of finding derivatives 高阶导数 Higher order derivatives 难点: Focal points 隐函数和由参数方程所确定的函数的导数 Derivation of implicit functions and parametric equations 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 微分中值定理与导数的应用 Mean Value Theorem and Applications of Derivatives 知识点: Knowledge Delivery 区间套定理 Theorem of nested interval 闭区间上连续函数的性质 Properties of continuous functions on a closed interval 微分中值定理 Differential mean value theorems 洛必达法则 L’ Hospital’s rules 泰勒公式 Taylor’s theorem 函数单调性、极值以及凹凸性质 Monotonicity, extreme values and convexity of functions 学习目标: Learning Objectives 了解: Recognize 区间套定理 Theorem of nested interval 闭区间上连续函数的性质 Properties of continuous functions on a closed interval 理解: Understand 微分中值定理及其证明 Differential mean value theorem and their proofs 掌握: Master 罗必达法则 L’ Hospital’s rules 函数单调性、极值以及凹凸性质 Monotonicity, extreme values and convexity of functions 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 拉格朗日定理 Lagrange’s theorem

难点：泰勒公式Taylor'stheoremFocal points支撑教学目标知识单元序号：41-1, 1-2, 1-3, 1-4Knowledge Unit No.SLOs Supported不定积分知识单元名称Unit TitleIndefinite Integrals不定积分的概念与性质Concepts and properties of indefinite integrals知识点：不定积分的换元法和分部积分法Knowledge DeliveryIntegration by substitution, integration by parts of indefiniteintegrals有理函数的积分Integrationofrational functions了解：不定积分的概念与性质RecognizeConcepts and properties of indefinite integrals理解：有理函数的积分学习目标：UnderstandIntegration ofrational functionsLearning Objectives不定积分的换元法和分部积分法掌握：Integration by substitution, integration by parts ofMasterindefinite integrals2-2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：不定积分的换元法和分部积分法Key PointsIntegrationby substitution,integrationbyparts of indefiniteintegrals难点：有理函数的积分Focal pointsIntegration of rational functions知识单元序号：支撑教学目标：51-1, 1-2, 1-3, 1-4SLOs SupportedKnowledge Unit No.知识单元名称定积分Unit TitleDefinite Integrals定积分的概念与性质Concepts and properties ofdefinite integrals微积分基本定理Fundamentaltheoremsofcalculus知识点：牛顿-莱布尼兹公式Newton-LeibnizformulaKnowledge Delivery定积分的换元法和分部积分法Integrationby substitution, integrationbyparts of definite integrals定积分的应用Applicationsofdefinite integrals反常积分Improperintegrals了解：定积分的概念与性质学习目标RecognizeConcepts and properties of definite integrals理解：Learning Objectives定积分的应用ApplicationsofdefiniteintegralsUnderstand反常积分Improperintegrals6/9

6 / 9 难点: Focal points 泰勒公式 Taylor’s theorem 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 不定积分 Indefinite Integrals 知识点: Knowledge Delivery 不定积分的概念与性质 Concepts and properties of indefinite integrals 不定积分的换元法和分部积分法 Integration by substitution, integration by parts of indefinite integrals 有理函数的积分 Integration of rational functions 学习目标: Learning Objectives 了解: Recognize 不定积分的概念与性质 Concepts and properties of indefinite integrals 理解: Understand 有理函数的积分 Integration of rational functions 掌握: Master 不定积分的换元法和分部积分法 Integration by substitution, integration by parts of indefinite integrals 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 不定积分的换元法和分部积分法 Integration by substitution, integration by parts of indefinite integrals 难点: Focal points 有理函数的积分 Integration of rational functions 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 定积分 Definite Integrals 知识点: Knowledge Delivery 定积分的概念与性质 Concepts and properties of definite integrals 微积分基本定理 Fundamental theorems of calculus 牛顿-莱布尼兹公式 Newton-Leibniz formula 定积分的换元法和分部积分法 Integration by substitution, integration by parts of definite integrals 定积分的应用 Applications of definite integrals 反常积分 Improper integrals 学习目标: Learning Objectives 了解: Recognize 定积分的概念与性质 Concepts and properties of definite integrals 理解: Understand 定积分的应用 Applications of definite integrals 反常积分 Improper integrals

微积分基本定理Fundamentaltheoremsofcalculus牛顿-莱布尼兹公式Newton-Leibnizformula掌握：定积分的换元法和分部积分法MasterIntegrationby substitution,integrationby parts ofdefinite integrals2-2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牛顿-莱布尼兹公式Newton-Leibnizformula重点：定积分的换元法和分部积分法Key PointsIntegration by substitution, integration by parts ofdefinite integrals难点：微积分基本定理FundamentaltheoremsofcalculusFocal points定积分的换元法Integrationbypartsindefiniteintegrals四、教学安排TeachingSchedule注：可根据实际情况增减行数Note: Please add/reduce lines based on subject.学时(周)Hour(Week)教学内容TeachingContent实践理论实验PBLEXPPRACLECT.函数与极限18000Functions and Limits导数与微分12000Derivative and Differential微分中值定理与导数的应用22000Mean Value Theorem and Applications ofDerivatives不定积分12000Indefinite Integrals定积分00016Definite Integrals00800总计Total五、教学方法TeachingMethodology注：可根据实际情况增减行数或修改内容Note:Please add/reduce lines orrevise contentbased on subject勾选Check教学方法与特色TeachingMethodology&Characters团课堂教学：板书与多媒体相结合、以板书为主7/9

7 / 9 掌握: Master 微积分基本定理 Fundamental theorems of calculus 牛顿-莱布尼兹公式 Newton-Leibniz formula 定积分的换元法和分部积分法 Integration by substitution, integration by parts of definite integrals 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 牛顿-莱布尼兹公式 Newton-Leibniz formula 定积分的换元法和分部积分法 Integration by substitution, integration by parts of definite integrals 难点: Focal points 微积分基本定理 Fundamental theorems of calculus 定积分的换元法 Integration by parts in definite integrals 四、教学安排 Teaching Schedule 注：可根据实际情况增减行数 Note: Please add/reduce lines based on subject. 教学内容 Teaching Content 学时(周)Hour(Week) 理论 LECT. 实验 EXP. 实践 PRAC. PBL 函数与极限 Functions and Limits 18 0 0 0 导数与微分 Derivative and Differential 12 0 0 0 微分中值定理与导数的应用 Mean Value Theorem and Applications of Derivatives 22 0 0 0 不定积分 Indefinite Integrals 12 0 0 0 定积分 Definite Integrals 16 0 0 0 总计 Total 80 0 0 0 五、教学方法 Teaching Methodology 注：可根据实际情况增减行数或修改内容 Note: Please add/reduce lines or revise content based on subject. 勾选 Check 教学方法与特色 Teaching Methodology & Characters  课堂教学：板书与多媒体相结合、以板书为主

Combination of blackboard writing and multimedia,mainlyblackboardwriting实践能力传授：理论与行业、实际案例相结合团Combining theory with industrial practical problems课程思政建设：知识讲授与德育相结合团Knowledge delivery with ethic educationPBL教学：口Problem-based learning其他：口Other:六、成绩评定Assessment注：可根据实际情况增减行数或修改内容Note: Please add/reduce lines or revise content based on subject.考核环节：环节负责人：刘艳杰平时BehaviorAssessment ContentDirectorLiu Yanjie给分形式课程总成绩比重(%):30百分制MarksResult TypePercentage (%)平时成绩，以学生平时课堂出勤、表现、课堂教师随机提问，学生平时作业完成情况综合评定，其中，学生平时课堂出勤、表现、课堂教师随机提问占比20%，学生平时作业完成情况占比80%.考核方式：According to instant answer to the teacher's questions, comprehensiveMeasuresreport and question performance, the mark is evaluated, where questionperformanceandinstantansweraccounts for1o%,assignmentsperformance (pre-lecture and post-lecture)accounts for 90%考核环节：环节负责人：刘艳杰期中Mid-termDirectorLiu YanjieAssessment Content给分形式课程总成绩比重(%)20百分制MarksResult TypePercentage (%)以闭卷形式进行2次阶段小测验（thresholdtest），每次120分钟考核方式：每次考试成绩占期中总成绩50%。MeasuresTwo threshold tests in the form of closed book, with 120 minutes eachtime.Each test score accounts for 50% of the total mid-term score考核环节：环节负责人：王晓敏期末FinalDirectorAssessment Content给分形式：课程总成绩比重(%):50百分制MarksResult TypePercentage (%)考核方式闭卷考试，考试时间120分钟。MeasuresClosedbookexamination, 120minutes.8/9

8 / 9 Combination of blackboard writing and multimedia, mainly blackboard writing  实践能力传授：理论与行业、实际案例相结合 Combining theory with industrial practical problems  课程思政建设：知识讲授与德育相结合 Knowledge delivery with ethic education ☐ PBL 教学： Problem-based learning ☐ 其他: Other: 六、成绩评定 Assessment 注：可根据实际情况增减行数或修改内容 Note: Please add/reduce lines or revise content based on subject. 考核环节: Assessment Content 平时 Behavior 环节负责人: Director 刘艳杰 Liu Yanjie 给分形式: Result Type 百分制 Marks 课程总成绩比重(%): Percentage (%) 30 考核方式: Measures 平时成绩，以学生平时课堂出勤、表现、课堂教师随机提问，学生 平时作业完成情况综合评定，其中，学生平时课堂出勤、表现、课 堂教师随机提问占比 20%, 学生平时作业完成情况占比 80%. According to instant answer to the teacher's questions, comprehensive report and question performance, the mark is evaluated, where question performance and instant answer accounts for 10%, assignments performance (pre-lecture and post-lecture) accounts for 90%. 考核环节: Assessment Content 期中 Mid-term 环节负责人: Director 刘艳杰 Liu Yanjie 给分形式: Result Type 百分制 Marks 课程总成绩比重(%): Percentage (%) 20 考核方式: Measures 以闭卷形式进行 2 次阶段小测验（threshold test），每次 120 分钟. 每次考试成绩占期中总成绩 50%。 Two threshold tests in the form of closed book, with 120 minutes each time. Each test score accounts for 50% of the total mid-term score. 考核环节: Assessment Content 期末 Final 环节负责人: Director 王晓敏 给分形式: Result Type 百分制 Marks 课程总成绩比重(%): Percentage (%) 50 考核方式: Measures 闭卷考试，考试时间 120 分钟。 Closed book examination, 120 minutes

七、改进机制ImprovementMechanism注：未尽事宜以教学团队以及学院教学指导委员会商定为准。Note: Matters not covered in this file shall be determined by TAB of SSTC, NEU.教学大纲改进机制SubjectSyllabusImprovementMechanism考核周期(年)修订周期(年)：44Check Period (YR)Revise Period (YR)课程负责人根据课程教学内容与人才培养目标组织课程团队讨论并修改教学大纲，报分管教学工作副院长审核后由执行院长批准。改进措施：The subjectcoordinatorshall beresponsibleforthesyllabusdiscussionMeasuresand improvement,andtherevisedversion shall be submittedtodeputydean (teaching affairs) for reviewing then to executive dean forapprovement.成绩评定改进机制AssessmentImprovementMechanism修订周期(年)：考核周期(年):11Check Period (YR)Revise Period (YR)课程负责人根据课程教学内容、课堂教学效果以及成绩分布，对课程教学方法和成绩评定环节进行改进，并同步优化评定办法。改进措施The subject coordinator shall revise the syllabus based on the teachingMeasurescontent, effect and result distribution while optimize the assessmentmeasures.9/9

9 / 9 七、改进机制 Improvement Mechanism 注：未尽事宜以教学团队以及学院教学指导委员会商定为准。 Note: Matters not covered in this file shall be determined by TAB of SSTC, NEU. 教学大纲改进机制 Subject Syllabus Improvement Mechanism 考核周期(年): Check Period (YR) 4 修订周期(年): Revise Period (YR) 4 改进措施: Measures 课程负责人根据课程教学内容与人才培养目标组织课程团队讨论 并修改教学大纲，报分管教学工作副院长审核后由执行院长批准。 The subject coordinator shall be responsible for the syllabus discussion and improvement, and the revised version shall be submitted to deputy dean (teaching affairs) for reviewing then to executive dean for approvement. 成绩评定改进机制 Assessment Improvement Mechanism 考核周期(年): Check Period (YR) 1 修订周期(年): Revise Period (YR) 1 改进措施: Measures 课程负责人根据课程教学内容、课堂教学效果以及成绩分布，对课 程教学方法和成绩评定环节进行改进，并同步优化评定办法。 The subject coordinator shall revise the syllabus based on the teaching content, effect and result distribution while optimize the assessment measures