东北大学：某学院计算机科学与技术专业《高等数学建模》课程教学大纲（一）

高等数学建模（一)教学大纲Mathematical Modelling ()Subject Syllabus一，课程信息SubjectInformation课程编号：开课学期：13100311003Subject IDSemester课程分类：所属课群：专业平台MT公共基础 GFCategorySection课程学分：总学时/周：580/14Credit PointsTotal Hours/Weeks理论学时：实验学时：800LECT. HoursEXP. HoursPBL学时:实践学时/周：00/0PBL HoursPRAC.Hours/Weeks东北大学悉尼智能科技学院开课学院：Sydney Smart适用专业：CST/CECollegeTechnology CollegeStreamNortheasternUniversity课程属性：课程模式：必修Compulsory互认EQVPatternMode中方课程协调人：成绩记载方式：李晓奇百分制MarksNEU CoordinatorResult Type无先修课程：RequisitesNone1. Mo Huixia, Li Xiaohua, Yuan Jianhua, Yuan Jianhua, Ai Wenbao,英文参考教材：Zhu Ping, Advanced Mathematics (I) & (Il), 2nd Edition, BeijingENTextbooksUniversityofPostsandTelecommunicationsPress,20182.RonLarson,ElementaryLinearAlgebra,CengageLearning,2017中文参考教材：同济大学数学系.高等数学（第七版）上、下册，高等教育出版社.2014CN Textbooks同济大学数学系，线性代数（第六版），高等教育出版社，2007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：单击或点击此处输SubjectDirectorLi Xiaoqi Submitted Date入日期。郭静梅、李晓奇、周蕊任课教师(含负责人)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Approved Date入日期。1/ 12

1 / 12 高等数学建模（一） 教学大纲 Mathematical Modelling (I) Subject Syllabus 一、课程信息 Subject Information 课程编号: Subject ID 3100311003 开课学期: Semester 1 课程分类: Category 公共基础 GF 所属课群: Section 专业平台 MT 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 0/0 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 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. Ron Larson, Elementary Linear Algebra, Cengage Learning, 2017. 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 同济大学数学系,线性代数(第六版), 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): SubjectDirector 李晓奇 Li Xiaoqi 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): 郭静梅、李晓奇、周蕊 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。Mathematical modeling is the foundation of science and engineering整体目标：courses.By learning the important concepts of limit, differential andOverall Objectiveintegral, it can lay a solid foundation for students to learn other subjectsand even professional courses. To cultivate students' strong practicalability,logical.rigorous and innovative thinking,as well as theconsciousness, interest and ability of solving practical problems byusing mathematical principles andmethods.Cultivatestudents tomaster the basictheories and methods of higher mathematics.especiallytheway of thinking,master knowledgeand skills,anddevelop creative ability at the same time.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 solving1-1complexengineeringproblemsininformationandcommunication and related fields through scientific andtechnological theories and engineering practical methods,aswell as the ability of doing academic cutting-edge project（1）专业目标：researchProfessional Ability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 solving1-2complexengineeringproblems in computer scienceand relatedfields through scientific and technological theories andengineering practical methods, as well as the ability of doingacademic 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 thesignificant meaningsoftheadvancedmathematics in depicting the practical engineering problems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 world2-3培养具有不畏困难、不惧失败、锲而不舍、敢于尝试、迎难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 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。 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. 1-2 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. （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. 2-3 培养具有不畏困难、不惧失败、锲而不舍、敢于尝试、迎难

而上的精神，并在学习过程中培养自己的细心和耐心的勇气和精神Cultivate the spirit of not fearing difficulties or failureperseverance, daring to try, and cultivate their own careful andpatient courage and spirit in the process of learning培养服务意识，具有“以人为本”的服务精神2-4Cultivate service consciousness and have the service spirit of"people-oriented"培养遵守法律、懂规则、守规则的新时代公民2-5Cultivate citizens of the new era who abide by the law,understand and obey the rules了解主要矛盾和次要矛盾，在面对复杂问题的时候要实事求是、抓住主要矛盾2-6Understandthe main contradiction and secondarycontradiction, seek truth from facts and grasp the maincontradiction in thefaceof complexproblems培养有条理和计划，做到心中有数、有条不紊、循序渐进地完成一项工作2-7Cultivate a sense oforder and plan,and completea work in anorderly andgradual manner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、工程知识：能够将数学、1-1掌握数学、自然科学、工程基础和专自然科学、工程基础和专业业知识，并使用其建立正确的数学、物知识用于解决复杂工程问理学等模型以解释复杂工程问题。题。Mastery of mathematics, natural science,Identify, formulate, research1-1, 1-2,engineering fundamentals and anliteratureandanalyze2-1 到 2-7engineering specialization to the solutioncomplex practical problemsof complex engineering problems with thereachingsubstantiatedestablishmentof correctmathematicalandfirstconclusionsusingphysical models.principles of mathematics andsciences2、问题分析：能够借助应2-1能够应用数学、自然科学和工程学的用统计学的基本原理、方法基本原理、方法和手段，分析、识别、和手段，识别、表达、并通表达本专业相关的复杂工程问题。过文献研究分析复杂实际问Capableof analyzing,identifyingand题，以获得有效结论。elaboratingcomplexpracticalproblems1-1, 1-2,Identify, formulate, researchrelated to this major with the applying of2-1到 2-7literatureandthebasicprinciples ofApplied Statistics.analyzecomplex practicalproblems2-2能够应用数学、自然科学和工程学的substantiatedreaching基本原理、方法和手段，针对实际复杂conclusionsusingfirst工程问题设计针对性的技术方案，并综principles of mathematics and合运用文献、科学基座和技术手段予以解决。sciences3/12

3 / 12 而上的精神，并在学习过程中培养自己的细心和耐心的勇气 和精神 Cultivate the spirit of not fearing difficulties or failure, perseverance, daring to try, and cultivate their own careful and patient courage and spirit in the process of learning 2-4 培养服务意识，具有“以人为本” 的服务精神 Cultivate service consciousness and have the service spirit of "people-oriented" 2-5 培养遵守法律、懂规则、守规则的新时代公民 Cultivate citizens of the new era who abide by the law, understand and obey the rules 2-6 了解主要矛盾和次要矛盾，在面对复杂问题的时候要实事求 是、抓住主要矛盾 Understand the main contradiction and secondary contradiction, seek truth from facts and grasp the main contradiction in the face of complex problems 2-7 培养有条理和计划，做到心中有数、有条不紊、循序渐进地 完成一项工作 Cultivate a sense of order and plan, and complete a work in an orderly and gradual manner 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、工程知识: 能够将数学、 自然科学、工程基础和专业 知识用于解决复杂工程问 题。 Identify, formulate, research literature and analyze complex practical problems reaching substantiated conclusions using first principles of mathematics and sciences. 1-1 掌握数学、自然科学、工程基础和专 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工程问题。 Mastery of mathematics, natural science, engineering fundamentals and an engineering specialization to the solution of complex engineering problems with the establishment of correct mathematical and physical models. 1-1, 1-2, 2-1 到 2-7 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. 1-1, 1-2, 2-1 到 2-7 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 thebasicprinciplesof applied statistics to design targetedschemesfor complexpracticalproblems,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: Flled in both CN and EN, extend or reduce based on the actual numbers of knowledge unit知识单元序号：支撑教学目标：11-1, 1-2SLOs SupportedKnowledge Unit No知识单元名称矩阵乘法和行列式Unit TitleMatrix multiplication and determinants线性方程组介绍，高斯消元法解方程组，矩阵的定义Introduction to linear equation system, Solving equations by Gausselimination,Definition ofmatrix矩阵的初等变换，矩阵的运算知识点：Elementarytransformation ofmatrix,Operations ofmatrixKnowledge Delivery矩阵运算性质，矩阵的逆Properties of matrix Operations,Inverse ofmatrix初等矩阵，行列式定义，行列式的运算及性质Elementary matrix,Definition of determinant,Operationsandproperties ofdeterminant了解：行列式定义，线性方程组RecognizeDefinition ofdeterminant, linear equation system高斯消元法，初等矩阵，找矩阵的逆，初等矩阵的性理解：质Gausselimination,ElementaryMatrix,Findingthe学习目标Understandinverse of a matrix,Properties of the elementaryLearning Objectivesmatrices:矩阵运算性质，行列式的运算及性质掌握：Properties of matrix operations,Operations andMasterpropertiesofdeterminant2-1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 indepictingthe practical engineeringproblems.2-3培养具有不畏困难、不惧失败、锲而不舍、敢于尝试、迎难而上的精神，并在学习过程中培养自己的细心和耐心的勇气和精神德育目标Cultivate the spirit of not fearing dificulties or failure, perseverance,Moral Objectivesdaring to try,and cultivate their own careful and patient courage andspirit in theprocess of learning2-4培养服务意识，具有“以人为本”的服务精神Cultivate service consciousness and have the service spirit of"people-oriented"4/12

4 / 12 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. 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 知识单元序号: Knowledge Unit No. 1 支撑教学目标: SLOs Supported 1-1，1-2 知识单元名称 Unit Title 矩阵乘法和行列式 Matrix multiplication and determinants 知识点: Knowledge Delivery 线性方程组介绍，高斯消元法解方程组，矩阵的定义 Introduction to linear equation system, Solving equations by Gauss elimination, Definition of matrix 矩阵的初等变换，矩阵的运算 Elementary transformation of matrix, Operations of matrix 矩阵运算性质，矩阵的逆 Properties of matrix Operations, Inverse of matrix 初等矩阵, 行列式定义，行列式的运算及性质 Elementary matrix, Definition of determinant, Operations and properties of determinant 学习目标: Learning Objectives 了解: Recognize 行列式定义, 线性方程组 Definition of determinant, linear equation system 理解: Understand 高斯消元法, 初等矩阵，找矩阵的逆，初等矩阵的性 质 Gauss elimination, Elementary Matrix, Finding the inverse of a matrix, Properties of the elementary matrices； 掌握: Master 矩阵运算性质，行列式的运算及性质 Properties of matrix operations, Operations and properties of determinant 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. 2-3 培养具有不畏困难、不惧失败、锲而不舍、敢于尝试、迎难而 上的精神，并在学习过程中培养自己的细心和耐心的勇气和精神 Cultivate the spirit of not fearing difficulties or failure, perseverance, daring to try, and cultivate their own careful and patient courage and spirit in the process of learning 2-4 培养服务意识，具有“以人为本” 的服务精神 Cultivate service consciousness and have the service spirit of "people-oriented

重点：高斯消元法，找矩阵的逆Key PointsGauss elimination,Finding the inverse of a matrix难点：矩阵运算性质，行列式的运算和性质Focal pointsPropertyofmatrixoperation,operation andpropertyofdeterminant知识单元序号支撑教学目标21-1, 1-2Knowledge Unit No.SLOs Supported知识单元名称向量空间与线性相关/无关Unit TitleVector space and linear dependence /independence向量，向量空间，向量子空间Vectors，VectorSpaces,SubspacesofVectorSpaces生成集和线性无关，基和维数SpanningSetsandLinearIndependence,BasisandDimension;知识点矩阵的秩和线性方程组RankofaMatrixandSystemsofLinearKnowledge DeliveryEquations;坐标和基变换Coordinates and Changeof Basis内积空间，正交基，施密特正交化过程InnerProductSpaces，OrthonormalBases,Gram-SchmidtProcess向量，向量空间，向量子空间,VectorsVectorspaces了解：SubspacesofVectorSpacesRecognize生成集，基和维数SpanningSetsBasisanddimension坐标和基变换；CoordinatesandChangeofBasis理解：内积，正交和正交集InnerProducts，OrthogonalandUnderstand学习目标：Orthonormal Sets;Learning Objectives线性相关和线性无关，Lineardependenceandlinearindependence;掌握：矩阵的秩和线性方程组RankofaMatrixandSystemsMasterof LinearEquations;施密特正交化过程Gram-SchmidtProcess2-2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 corecompetitiveness in the area of the China engineering in the world.2-3培养具有不畏困难、不惧失败、锲而不舍、敢于尝试、迎难而德育目标上的精神，并在学习过程中培养自己的细心和耐心的勇气和精神Moral ObjectivesCultivate the spirit of not fearing difficulties or failure, perseverance,daring to try, and cultivate their own careful and patient courage andspirit intheprocess of learning2-4培养服务意识，具有“以人为本”的服务精神Cultivate service consciousness and have the service spirit of"people-oriented"线性相关和线性无关Lineardependenceand linearindependence;重点：矩阵的秩和线性方程组Rankof aMatrixandSystemsofLinearKey PointsEquations;5/12

5 / 12 重点: Key Points 高斯消元法, 找矩阵的逆 Gauss elimination, Finding the inverse of a matrix 难点: Focal points 矩阵运算性质，行列式的运算和性质 Property of matrix operation, operation and property of determinant 知识单元序号: Knowledge Unit No. 2 支撑教学目标: SLOs Supported 1-1，1-2 知识单元名称 Unit Title 向量空间与线性相关/无关 Vector space and linear dependence /independence 知识点: Knowledge Delivery 向量,向量空间,向量子空间 Vectors, Vector Spaces, Subspaces of Vector Spaces 生成集和线性无关, 基和维数 Spanning Sets and Linear Independence，Basis and Dimension； 矩阵的秩和线性方程组 Rank of a Matrix and Systems of Linear Equations； 坐标和基变换 Coordinates and Change of Basis 内积空间，正交基, 施密特正交化过程 Inner Product Spaces, Orthonormal Bases, Gram-Schmidt Process 学习目标: Learning Objectives 了解: Recognize 向量,向量空间,向量子空间,Vectors, Vector spaces, Subspaces of Vector Spaces 生成集,基和维数 Spanning Sets, Basis and dimension; 理解: Understand 坐标和基变换；Coordinates and Change of Basis； 内积, 正交和正交集 Inner Products, Orthogonal and Orthonormal Sets； 掌握: Master 线性相关和线性无关,Linear dependence and linear independence; 矩阵的秩和线性方程组 Rank of a Matrix and Systems of Linear Equations； 施密特正交化过程 Gram-Schmidt Process 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. 2-3 培养具有不畏困难、不惧失败、锲而不舍、敢于尝试、迎难而 上的精神，并在学习过程中培养自己的细心和耐心的勇气和精神 Cultivate the spirit of not fearing difficulties or failure, perseverance, daring to try, and cultivate their own careful and patient courage and spirit in the process of learning 2-4 培养服务意识，具有“以人为本” 的服务精神 Cultivate service consciousness and have the service spirit of "people-oriented" 重点: Key Points 线性相关和线性无关 Linear dependence and linear independence; 矩阵的秩和线性方程组 Rank of a Matrix and Systems of Linear Equations；

难点：施密特正交化过程Gram-SchmidtProcessFocal points知识单元序号：支撑教学目标：31-1, 1-2Knowledge Unit No.SLOs Supported知识单元名称线性变换及特征向量Unit TitleLinear transformation and eigenvector线性变换的介绍，相似矩阵introductiontoLinearTransformations,Similar Matrices:特征值与特征向量，对角化Eigenvalues andEigenvectors，Diagonalization知识点：对称矩阵和正交对角化SymmetricMatricesandorthogonalKnowledge DeliveryDiagonalization实二次型和其矩阵，实二次型的标准型，正定二次型Realquadraticformand its matrix,Canonicalformof realquadraticform,PositiveDefiniteQuadraticForm线性变换的定义DefinitionofaLinearTransformation了解：对称矩阵的定义DefinitionofaSymmetricMatrices：Recognize实二次型和其矩阵Realquadraticformanditsmatrix二次型的对角型Diagonalformofquadraticform；理解：对称矩阵的性质propertiesofSymmetricMatrices；学习目标：Understand正交对角化orthogonalDiagonalizationLearning Objectives特征值与特征向量EigenvaluesandEigenvectors：掌握：正交变换转化二次型为对角型ChangingquadraticMasterform intodiagonal form by Orthogonal Transformation;正定二次型PositiveDefiniteQuadraticForm2-1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 indepicting the practical engineering problems.2-5培养遵守法律、懂规则、守规则的新时代公民Cultivate citizens of the new era who abide by the law,understand and德育目标obey the rulesMoral Objectives2-6了解主要矛盾和次要矛盾，在面对复杂问题的时候要实事求是、抓住主要矛盾Understand themain contradiction and secondary contradiction,seektruth from facts and grasp the main contradiction in the face ofcomplexproblems找特征值与特征向量FindingEigenvaluesandEigenvectors；重点：对称矩阵的性质propertiesof SymmetricMatrices；Key Points正交对角化orthogonalDiagonalization难点：矩阵对角化MatrixDiagonalizable6/12

6 / 12 难点: Focal points 施密特正交化过程 Gram-Schmidt Process 知识单元序号: Knowledge Unit No. 3 支撑教学目标: SLOs Supported 1-1，1-2 知识单元名称 Unit Title 线性变换及特征向量 Linear transformation and eigenvector 知识点: Knowledge Delivery 线性变换的介绍,相似矩阵 introduction to Linear Transformations, Similar Matrices； 特征值与特征向量, 对角化 Eigenvalues and Eigenvectors, Diagonalization 对称矩阵和正交对角化 Symmetric Matrices and orthogonal Diagonalization 实二次型和其矩阵,实二次型的标准型,正定二次型 Real quadratic form and its matrix, Canonical form of real quadratic form, Positive Definite Quadratic Form 学习目标: Learning Objectives 了解: Recognize 线性变换的定义 Definition of a Linear Transformation 对称矩阵的定义 Definition of a Symmetric Matrices； 实二次型和其矩阵 Real quadratic form and its matrix； 二次型的对角型 Diagonal form of quadratic form； 理解: Understand 对称矩阵的性质 properties of Symmetric Matrices； 正交对角化 orthogonal Diagonalization 掌握: Master 特征值与特征向量 Eigenvalues and Eigenvectors； 正交变换转化二次型为对角型 Changing quadratic form into diagonal form by Orthogonal Transformation; 正定二次型 Positive Definite Quadratic Form 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. 2-5 培养遵守法律、懂规则、守规则的新时代公民 Cultivate citizens of the new era who abide by the law, understand and obey the rules 2-6 了解主要矛盾和次要矛盾，在面对复杂问题的时候要实事求是、 抓住主要矛盾 Understand the main contradiction and secondary contradiction, seek truth from facts and grasp the main contradiction in the face of complex problems 重点: Key Points 找特征值与特征向量 Finding Eigenvalues and Eigenvectors； 对称矩阵的性质 properties of Symmetric Matrices； 正交对角化 orthogonal Diagonalization 难点: 矩阵对角化 Matrix Diagonalizable

正交变换转化二次型为对角型ChangingQuadraticFormintoFocalpointsDiagonal Form by Orthogonal Transformation;正定二次型PositiveDefiniteQuadraticForm；知识单元序号支撑教学目标：41-1, 1-2Knowledge Unit No.SLOs Supported函数性质及其与测量和物理结果解释的关系知识单元名称Functions and their relationship to measurement and the interpretationUnit Titleofphysical results数列极限性质LimitsofSequences知识点：函数极限性质TheLimitofaFunctionKnowledge Delivery无穷及无穷性质InfinitesimalandInfiniteproperties连续函数及其性质ContinuousFunctionsanditsproperties了解：数列以及函数极限的定义RecognizeThe definition of limit ofa sequence and afunction学习目标：理解：连续函数的定义以及性质UnderstandDefinition and properties of continuous functionsLearning Objectives掌握：无穷及无穷性质MasterInfinitesimal and Infiniteproperties2-2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 corecompetitiveness in the area of the China engineering in the world2-5培养遵守法律、懂规则、守规则的新时代公民德育目标Cultivate citizens of the new era who abide by the law, understand andMoral Objectivesobey the rules2-6了解主要矛盾和次要矛盾，在面对复杂问题的时候要实事求是、抓住主要矛盾Understand the main contradiction and secondarycontradiction,seektruth from facts and grasp the main contradiction in the face ofcomplexproblems重点：连续函数的定义以及性质Key PointsDefinition and properties of continuous functions难点：无穷及无穷性质Focal pointsInfinitesimal and Infinite properties知识单元序号支撑教学目标51-1, 1-2SLOs SupportedKnowledgeUnitNo知识单元名称导数与微分Unit TitleDerivative and Differential导数的概念以及应用ConceptofDerivativesand itsapplications知识点：求导数以及高阶导数的法则Knowledge DeliveryRules of Finding Derivatives, Higher Order Derivatives隐函数以及参数方程的求导数法则7/12

7 / 12 Focal points 正交变换转化二次型为对角型 Changing Quadratic Form into Diagonal Form by Orthogonal Transformation; 正定二次型 Positive Definite Quadratic Form； 知识单元序号: Knowledge Unit No. 4 支撑教学目标: SLOs Supported 1-1，1-2 知识单元名称 Unit Title 函数性质及其与测量和物理结果解释的关系 Functions and their relationship to measurement and the interpretation of physical results 知识点: Knowledge Delivery 数列极限性质 Limits of Sequences 函数极限性质 The Limit of a Function 无穷及无穷性质 Infinitesimal and Infinite properties 连续函数及其性质 Continuous Functions and its properties 学习目标: Learning Objectives 了解: Recognize 数列以及函数极限的定义 The definition of limit of a sequence and a function 理解: Understand 连续函数的定义以及性质 Definition and properties of continuous functions 掌握: Master 无穷及无穷性质 Infinitesimal and Infinite properties 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. 2-5 培养遵守法律、懂规则、守规则的新时代公民 Cultivate citizens of the new era who abide by the law, understand and obey the rules 2-6 了解主要矛盾和次要矛盾，在面对复杂问题的时候要实事求是、 抓住主要矛盾 Understand the main contradiction and secondary contradiction, seek truth from facts and grasp the main contradiction in the face of complex problems 重点: Key Points 连续函数的定义以及性质 Definition and properties of continuous functions 难点: Focal points 无穷及无穷性质 Infinitesimal and Infinite properties 知识单元序号: Knowledge Unit No. 5 支撑教学目标: SLOs Supported 1-1，1-2 知识单元名称 Unit Title 导数与微分 Derivative and Differential 知识点: Knowledge Delivery 导数的概念以及应用 Concept of Derivatives and its applications 求导数以及高阶导数的法则 Rules of Finding Derivatives, Higher Order Derivatives 隐函数以及参数方程的求导数法则

Derivation of Implicit Functions and ParametricEquations了解：导数的概念以及应用Concept of Derivatives and its applicationsRecognize理解：求导数以及高阶导数的法则学习目标：UnderstandRules of Finding Derivatives, Higher Order DerivativesLearning Objectives隐函数以及参数方程的求导数法则掌握：Derivation of Implicit FunctionssandParametricMasterEquations2-1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 thesignificant meanings of the advanced mathematics indepictingthepractical engineeringproblems2-6了解主要矛盾和次要矛盾，在面对复杂问题的时候要实事求是、抓住主要矛盾德育目标Understand the main contradiction and secondary contradiction, seekMoral Objectivestruthfromfactsand grasp themain contradictionin theface ofcomplexproblems2-7培养有条理和计划，做到心中有数、有条不紊、循序渐进地完成一项工作Cultivate a sense of order and plan,and complete a work inan orderlyand gradual manner重点：求导数以及高阶导数的法则Key PointsRules of Finding Derivatives, Higher Order Derivatives难点：隐函数以及参数方程的求导数法则Focal pointsDerivation ofImplicitFunctions andParametricEquations知识单元序号支撑教学目标：61-1, 1-2KnowledgeUnitNoSLOs Supported微分中值定理及其应用知识单元名称Unit TitleMeanvaluetheoremand its applications罗尔定理、微分中值定理Rolletheorem,Meanvaluetheorem知识点：洛必达法则、泰勒定理Lhospital'srule，TaylortheoremKnowledge Delivery极值及其应用问题Extremevalueanditsapplications函数单调性及其应用Monotonicityanditsapplications了解:罗尔定理、微分中值定理RecognizeRolle theorem, Mean value theorem学习目标：理解：极值及其应用问题UnderstandExtreme value and its applicationsLearning Objectives掌握：洛必达法则MasterL'hospital's rule2-2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。德育目标Understand the technology development, key techniques and the coreMoral Objectivescompetitiveness in the area of the China engineering in the world2-5培养遵守法律、懂规则、守规则的新时代公民Cultivate citizens ofthe new era who abideby thelaw,understand and8/12

8 / 12 Derivation of Implicit Functions and Parametric Equations 学习目标: Learning Objectives 了解: Recognize 导数的概念以及应用 Concept of Derivatives and its applications 理解: Understand 求导数以及高阶导数的法则 Rules of Finding Derivatives, Higher Order Derivatives 掌握: Master 隐函数以及参数方程的求导数法则 Derivation of Implicit Functions and Parametric Equations 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. 2-6 了解主要矛盾和次要矛盾，在面对复杂问题的时候要实事求是、 抓住主要矛盾 Understand the main contradiction and secondary contradiction, seek truth from facts and grasp the main contradiction in the face of complex problems 2-7 培养有条理和计划，做到心中有数、有条不紊、循序渐进地完 成一项工作 Cultivate a sense of order and plan, and complete a work in an orderly and gradual manner 重点: Key Points 求导数以及高阶导数的法则 Rules of Finding Derivatives, Higher Order Derivatives 难点: Focal points 隐函数以及参数方程的求导数法则 Derivation of Implicit Functions and Parametric Equations 知识单元序号: Knowledge Unit No. 6 支撑教学目标: SLOs Supported 1-1，1-2 知识单元名称 Unit Title 微分中值定理及其应用 Mean value theorem and its applications 知识点: Knowledge Delivery 罗尔定理、微分中值定理 Rolle theorem, Mean value theorem 洛必达法则、泰勒定理 L'hospital's rule， Taylor theorem 极值及其应用问题 Extreme value and its applications 函数单调性及其应用 Monotonicity and its applications 学习目标: Learning Objectives 了解: Recognize 罗尔定理、微分中值定理 Rolle theorem, Mean value theorem 理解: Understand 极值及其应用问题 Extreme value and its applications 掌握: Master 洛必达法则 L'hospital's rule 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. 2-5 培养遵守法律、懂规则、守规则的新时代公民 Cultivate citizens of the new era who abide by the law, understand and

obey the rules2-6了解主要矛盾和次要矛盾，在面对复杂问题的时候要实事求是、抓住主要矛盾Understand themain contradiction and secondary contradiction,seektruth from facts and grasp the main contradiction in the face ofcomplexproblems重点：函数单调性及其应用Key PointsMonotonicityand its applications难点：洛必达法则Focal pointsL'hospital's rule知识单元序号：支撑教学目标：71-1, 1-2Knowledge Unit No.SLOs Supported知识单元名称积分及其性质Unit TitleIntegral and its properties不定积分的概念与性质Concepts and Properties of Indefinite Integrals不定积分的求法Operation Rules of Indefinite Integrals定积分的概念与性质Concepts andPropertiesof DefiniteIntegrals知识点：微积分基本定理TheFundamental Theorems of CalculusKnowledge Delivery定积分的换元和分部积分法Integration by Substitution and Parts in Definite Integrals反常积分Improper Integrals定积分的几何应用Applications of Definite Integrals不定积分、定积分的概念与性质了解:Concepts and Properties of Indefinite Integrals andRecognizeIntegrals不定积分的求法理解：Operation Rules of Indefinite IntegralsUnderstand反常积分学习目标：Improper IntegralsLearning Objectives微积分基本定理TheFundamental Theorems of Calculus定积分的换元和分部积分法掌握：Integration by Substitution andPartsinDefiniteMasterIntegrals定积分的几何应用Applications ofDefinite Integrals德育目标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9/12

9 / 12 obey the rules 2-6 了解主要矛盾和次要矛盾，在面对复杂问题的时候要实事求是、 抓住主要矛盾 Understand the main contradiction and secondary contradiction, seek truth from facts and grasp the main contradiction in the face of complex problems 重点: Key Points 函数单调性及其应用 Monotonicity and its applications 难点: Focal points 洛必达法则 L'hospital's rule 知识单元序号: Knowledge Unit No. 7 支撑教学目标: SLOs Supported 1-1，1-2 知识单元名称 Unit Title 积分及其性质 Integral and its properties 知识点: Knowledge Delivery 不定积分的概念与性质 Concepts and Properties of Indefinite Integrals 不定积分的求法 Operation Rules of Indefinite Integrals 定积分的概念与性质 Concepts and Properties of Definite Integrals 微积分基本定理 The Fundamental Theorems of Calculus 定积分的换元和分部积分法 Integration by Substitution and Parts in Definite Integrals 反常积分 Improper Integrals 定积分的几何应用 Applications of Definite Integrals 学习目标: Learning Objectives 了解: Recognize 不定积分、定积分的概念与性质 Concepts and Properties of Indefinite Integrals and Integrals 理解: Understand 不定积分的求法 Operation Rules of Indefinite Integrals 反常积分 Improper Integrals 掌握: Master 微积分基本定理 The Fundamental Theorems of Calculus 定积分的换元和分部积分法 Integration by Substitution and Parts in Definite Integrals 定积分的几何应用 Applications of Definite Integrals 德育目标 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

Moral Objectives心竞争力的重要意义。Understand the technology development, key techniques and the corecompetitiveness in the area of the China engineering in the world.2-6了解主要矛盾和次要矛盾，在面对复杂问题的时候要实事求是、抓住主要矛盾Understand themain contradiction and secondary contradiction, seektruth from facts and grasp the main contradiction in the face ofcomplexproblems2-7培养有条理和计划，做到心中有数、有条不紊、循序渐进地完成一项工作Cultivate a sense of order and plan,and completea work in an orderlyand gradual manner重点：不定积分的求法Key PointsOperation Rules of Indefinite Integrals微积分基本定理难点：The Fundamental Theorems of CalculusFocal points定积分的分部积分法IntegrationbyParts inDefiniteIntegrals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Teaching Content理论实验实践PBLLECTEXP.PRAC矩阵乘法和行列式13000Matrix multiplication and determinants向量空间与线性相关性质9000Vectorspaceandlineardependenceproperties线性变换及特征向量0080Linear transformation and eigenvector函数极限和连续00014Functions limits and continuous functions微分中值定理及其应用00012Meanvaluetheoremanditsapplications导数与微分0060Derivative and Differential积分及其性质00180Integral and its properties00总计Total80010 /12

10 / 12 Moral Objectives 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. 2-6 了解主要矛盾和次要矛盾，在面对复杂问题的时候要实事求是、 抓住主要矛盾 Understand the main contradiction and secondary contradiction, seek truth from facts and grasp the main contradiction in the face of complex problems 2-7 培养有条理和计划，做到心中有数、有条不紊、循序渐进地完 成一项工作 Cultivate a sense of order and plan, and complete a work in an orderly and gradual manner 重点: Key Points 不定积分的求法 Operation Rules of Indefinite Integrals 难点: Focal points 微积分基本定理 The Fundamental Theorems of Calculus 定积分的分部积分法 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 矩阵乘法和行列式 Matrix multiplication and determinants 13 0 0 0 向量空间与线性相关性质 Vector space and linear dependence properties 9 0 0 0 线性变换及特征向量 Linear transformation and eigenvector 8 0 0 0 函数极限和连续 Functions limits and continuous functions 14 0 0 0 微分中值定理及其应用 Mean value theorem and its applications 12 0 0 0 导数与微分 Derivative and Differential 6 0 0 0 积分及其性质 Integral and its properties 18 0 0 0 总计 Total 80 0 0 0