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）.pdf

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；