东北大学：某学院应用统计学专业《微分方程》课程教学大纲

微分方程教学大纲Differential EquationsSubject Syllabus一，课程信息SubjectInformation课程编号：开课学期：33100313003SemesterSubject ID课程分类：所属课群：专业基础MF专业教育PACategorySection课程学分：总学时/周：3.556/10Credit PointsTotal Hours/Weeks理论学时：实验学时：560LECT. 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：应用统计学ASCollegeTechnology CollegeStreamNortheasternUniversity课程模式：课程属性：必修Compulsory互认EQVPatternMode刘超中方课程协调人：成绩记载方式：百分制MarksNEU CoordinatorLiu ChaoResult Type数学分析与建模（一），数学分析与建模（二)先修课程：Mathematical Analysis and Modelling (),RequisitesMathematical Analysis andModelling (Il)英文参考教材：VladimirI.Arnold,OrdinaryDifferential Equations,World ScienceENTextbooksPress, 2004.中文参考教材：王高雄，常微分方程，高等教育出版社，2004CN Textbooks教学资源：https:/sstc.cloudcampus.com.cn/course/view.php?id=18Resources刘超课程负责人(撰写人)提交日期：单击或点击此处输Liu Chao入日期。SubjectDirectorSubmitted Date刘超任课教师(含负责人)：Liu ChaoTaught by审核人：批准人：韩鹏史闻博Checked byApprovedby批准日期：单击或点击此处输入日期。ApprovedDate1/11

1 / 11 微分方程 教学大纲 Differential Equations Subject Syllabus 一、课程信息 Subject Information 课程编号: Subject ID 3100313003 开课学期: Semester 3 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 3.5 总学时/周: Total Hours/Weeks 56/10 理论学时: LECT. Hours 56 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 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 刘超 Liu Chao 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），数学分析与建模（二） Mathematical Analysis and Modelling (I), Mathematical Analysis and Modelling (II) 英文参考教材: EN Textbooks Vladimir I. Arnold, Ordinary Differential Equations, World Science Press, 2004. 中文参考教材: CN Textbooks 王高雄，常微分方程， 高等教育出版社，2004. 教学资源: Resources https://sstc.cloudcampus.com.cn/course/view.php?id=18 课程负责人(撰写人): SubjectDirector 刘超 Liu Chao 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 刘超 Liu Chao 审核人: Checked by 韩鹏 批准人: Approvedby 史闻博 批准日期: Approved Date 单击或点击此处输 入日期

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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微分方程是应用统计专业课程的基础，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。培养学生掌握微分方程的基本理论和方法，尤其是思维方式，掌握知识技能的同时发展创造能力。Differential equation is the foundation of science and engineering整体目标：courses.By learning the important concepts of limit, differential andOverallObjectiveintegral, 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,aswell as theconsciousness, interest and ability of solving practical problems byusing mathematical principles andmethods.Cultivatestudents tomaster the basic theories and methods of differential equationespeciallytheway of thinking,masterknowledgeand skills,anddevelop creativeabilityat 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 of the specialized knowledge and skills in statistics anddata analysis, intelligent simulation modeling technology,quantitativemanagementoptimizationtechnology,experimental design and analysis, project management and（1）专业目标：decision-making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Professional Ability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 in1-2applied statistics, and capable of creatively solving complexengineering problems in applied statistics and related fieldsthrough 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 theadvancedmathematicsindepictingthepracticalengineeringproblems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 world3/ 11

3 / 11 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 微分方程是应用统计专业课程的基础，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。 培养学生掌握微分方程的基本理论和方法，尤其是思维方式，掌握 知识技能的同时发展创造能力。 Differential equation 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 differential equation, 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

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2-3Cultivate 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 thelaw,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2-6contradictionandUnderstandthemainsecondarycontradiction, seek truth from facts and grasp the maincontradictioninthefaceofcomplexproblems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2-7Cultivatea sense of order 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。1-1, 1-2,ApplyknowledgeofCapable of deductive reasoning,accurate2-1到 2-7mathematics, natural science,calculation, analysis and induction andandfundamentalsanabstract thinking.Establishing correctengineering specialization tomathematical and physical models with theprofessional knowledge of mathematics,thesolutionofcomplexengineering problems.natural science,etc.to solve complexpracticalproblems2、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Capable of analyzing,identifying and1-1, 1-2,题，以获得有效结论。elaboratingcomplex practical problems2-1到 2-7Identify,formulate,researchrelatedtothismajor withthe applying ofliteratureandanalyzethebasicprinciples of Applied Statisticscomplex practical problems2-2能够应用数学、自然科学和工程学的reachingsubstantiated基本原理、方法和手段，针对实际复杂firstconclusionsusing工程问题设计针对性的技术方案，并综4/11

4 / 11 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" 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、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, 2-1 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 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principles of mathematics and解决。sciences.Capable of drawing on the basic principlesof applied statistics to design targetedschemesforcomplexpracticalproblems.and using literature, scientific theories andtechnicalmeansto solvethem.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 ofknowledge unit(1）理论教学Lecture知识单元序号支撑教学目标11-1, 1-2Knowledge Unit No.SLOs Supported知识单元名称-阶微分方程的初等解法Unit TitleFundamental solving method of the first order differential equation变量分离方程的概念与解法；贝努利方程解法；Definition and solvingmethodofvariable separableequationSolving method of Bernulli equation线性微分方程与常数变易法：知识点：Linear differential equation and constant variation methodKnowledge Delivery恰当微分方程与积分因子；Appropriatedifferential equation and integral coefficient一阶隐式微分方程与参数表示。Thefirst order implicit differential equation and parametricrepresentation变量分离方程的概念与解法：贝努利方程解法；了解：Definition and solving method of variable separableRecognizeequationSolving method of Bernulli equation学习目标：线性微分方程与常数变易法：理解：Linear differential equation andLearning ObjectivesconstantvariationUnderstandmethod恰当微分方程与积分因子；掌握：differentialandintegralAppropriateequationMastercoefficient2-1理解微分方程理论知识对于刻画工程实践问题的重要意义。Understandthe significantmeanings of thedifferential equation indepicting thepractical engineeringproblems2-3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 ObjectivesUnderstandthetechnologydevelopment,keytechniques andthecorecompetitiveness in the area ofthe China engineering in theworld2-4培养具有不畏困难、不惧失败、锲而不舍、敢于尝试、迎难而5/11

5 / 11 principles of mathematics and sciences. 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. 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 知识单元名称 Unit Title 一阶微分方程的初等解法 Fundamental solving method of the first order differential equation 知识点: Knowledge Delivery 变量分离方程的概念与解法；贝努利方程解法； Definition and solving method of variable separable equation Solving method of Bernulli equation 线性微分方程与常数变易法； Linear differential equation and constant variation method 恰当微分方程与积分因子； Appropriate differential equation and integral coefficient 一阶隐式微分方程与参数表示。 The first order implicit differential equation and parametric representation 学习目标: Learning Objectives 了解: Recognize 变量分离方程的概念与解法；贝努利方程解法； Definition and solving method of variable separable equation Solving method of Bernulli equation 理解: Understand 线性微分方程与常数变易法； Linear differential equation and constant variation method 掌握: Master 恰当微分方程与积分因子； Appropriate differential equation and integral coefficient 德育目标 Moral Objectives 2-1 理解微分方程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 differential equation in depicting the practical engineering problems. 2-3 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. 2-4 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 andspirit in the process of learning重点：恰当微分方程与积分因子；Key PointsAppropriatedifferential equationand integral coefficient阶隐式微分方程与参数表示。难点：The first order implicit differential equation and parametricFocal pointsrepresentation知识单元序号：支撑教学目标：21-1, 1-2Knowledge Unit No.SLOs Supported知识单元名称阶微分方程的解的存在定理Unit TitleExistence theorem of solution of the first order differential equation解的存在唯一性定理与逐步逼近法（存在唯一性定理，近似计算和误差估计）Existenceofunique solution and approximation (Existence theoremof知识点：uniquesolution,approximatecalculation,errorestimation)Knowledge Delivery解对初值的连续性和可微性定理；Continuity of solution depending on initial value and differentiabilitytheorem了解:解的存在唯一性定理Existence theorem of unique solutionRecognize学习目标理解：解的近似计算Learning ObjectivesUnderstandApproximate calculation of solution掌握：解的误差估计MasterErrorestimationof solution2-1理解微分方程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 differential equation indepictingthepractical engineeringproblems2-4培养服务意识，具有“以人为本”的服务精神德育目标Cultivate service consciousness and have the service spirit ofMoral Objectives"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 bythelaw,understand andobey the rules重点：解对初值的连续性Key PointsContinuity of solutiondependingon initial value难点：解可微性定理；Focal pointsDifferentiability theorem of solution.支撑教学目标知识单元序号31-1, 1-2Knowledge Unit No.SLOs Supported知识单元名称高阶微分方程Unit TitleHigherorderdifferential equation6/11

6 / 11 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 重点: Key Points 恰当微分方程与积分因子； Appropriate differential equation and integral coefficient 难点: Focal points 一阶隐式微分方程与参数表示。 The first order implicit differential equation and parametric representation 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 一阶微分方程的解的存在定理 Existence theorem of solution of the first order differential equation 知识点: Knowledge Delivery 解的存在唯一性定理与逐步逼近法（存在唯一性定理，近似计算和 误差估计） Existence of unique solution and approximation (Existence theorem of unique solution, approximate calculation, error estimation) 解对初值的连续性和可微性定理； Continuity of solution depending on initial value and differentiability theorem. 学习目标: Learning Objectives 了解: Recognize 解的存在唯一性定理 Existence theorem of unique solution 理解: Understand 解的近似计算 Approximate calculation of solution 掌握: Master 解的误差估计） Error estimation of solution 德育目标 Moral Objectives 2-1 理解微分方程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 differential equation in depicting the practical engineering problems. 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 重点: Key Points 解对初值的连续性 Continuity of solution depending on initial value 难点: Focal points 解可微性定理； Differentiability theorem of solution. 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 高阶微分方程 Higher order differential equation

线性微分方程的一般理论；General theoryof lineardifferential equation齐线性方程的解的性质与结构；Thepropertyand structureof solutionofhomogeneous linearequation知识点：非齐线性方程与常数变易法：Knowledge DeliveryNonhomogeneous linear equation and constant variation method常系数线性微分方程的解法；Solving method of ordinary linear differential equation with constantcoefficient了解：线性微分方程的一般理论；RecognizeGeneral theory of linear differential equation常系数齐线性方程和欧拉方程；理解：学习目标：Homogeneous equation with constant coefficient andUnderstandLearning ObjectivesEuler equation常系数线性微分方程的解法：掌握：Solving method of ordinary linear differential equationMasterwith constant coefficient2-2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.2-5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 themain contradiction and secondary contradiction,seektruthfrom facts and grasp themain contradiction in the face ofcomplexproblems非齐线性方程的比较系数法与拉普拉斯变换法：重点：Comparison coefficient method Laplacian variation method ofKey Pointsnonhomogeneous linear equation高阶微分方程的降阶和幂级数解法；难点：Order reduction and power series solving method of higher orderFocal pointsdifferential equation知识单元序号支撑教学目标：41-1, 1-2Knowledge Unit No.SLOs Supported知识单元名称线性微分方程组Unit TitleLinear differential equations线性微分方程组的一般理论：General theory of linear differential equations知识点齐线性微分方程组；Knowledge DeliveryHomogeneous linear differential equations常系数线性微分方程组；7/11

7 / 11 知识点: Knowledge Delivery 线性微分方程的一般理论； General theory of linear differential equation 齐线性方程的解的性质与结构； The property and structure of solution of homogeneous linear equation 非齐线性方程与常数变易法； Nonhomogeneous linear equation and constant variation method 常系数线性微分方程的解法； Solving method of ordinary linear differential equation with constant coefficient 学习目标: Learning Objectives 了解: Recognize 线性微分方程的一般理论； General theory of linear differential equation 理解: Understand 常系数齐线性方程和欧拉方程； Homogeneous equation with constant coefficient and Euler equation 掌握: Master 常系数线性微分方程的解法； Solving method of ordinary linear differential equation with constant coefficient 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 非齐线性方程的比较系数法与拉普拉斯变换法； Comparison coefficient method Laplacian variation method of nonhomogeneous linear equation 难点: Focal points 高阶微分方程的降阶和幂级数解法； Order reduction and power series solving method of higher order differential equation 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 线性微分方程组 Linear differential equations 知识点: Knowledge Delivery 线性微分方程组的一般理论； General theory of linear differential equations 齐线性微分方程组； Homogeneous linear differential equations 常系数线性微分方程组；

Linear differential equations with constant coefficient了解：线性微分方程组的一般理论；RecognizeGeneral theory of linear differential equations学习目标：理解：非齐线性微分方程组：Learning ObjectivesUnderstandNonhomogeneous lineardifferential equation掌握：矩阵指数expA的定义和性质；MasterDefinition and propertiesofmatrixexponent2-1理解微分方程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 differential equation indepicting 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，抓住主要矛盾德育目标Understand themain contradiction and secondary contradiction,seekMoral Objectivestruthfrom facts and grasp themain 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 complete a work in an orderlyand gradual manner重点：非齐线性微分方程组；Key PointsNonhomogeneous linear differential equation难点：基解矩阵的计算公式。Focal pointsCalculus formula of fundamental matrix知识单元序号支撑教学目标：51-1, 1-2Knowledge Unit No.SLOs Supported知识单元名称非线性微分方程Unit TitleNonlinear differential equations解的稳定性概念；Definition of stabilityof solution常微分方程组的存在唯一性定理：知识点：Existence of unigue solution ofordinarydifferential equationsKnowledge Delivery李雅普诺夫稳定性；Lyapunov stability稳定、不稳定、渐近稳定的概念。Definitionofstability,instability,appropriatestability了解：解的稳定性概念；RecognizeDefinition of stabilityof solution学习目标：理解：稳定、不稳定、渐近稳定的概念。Learning ObjectivesUnderstandDefinition of stability, instability, appropriate stability掌握：李雅普诺夫稳定性；MasterLyapunov stability2-2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 core8/11

8 / 11 Linear differential equations with constant coefficient 学习目标: Learning Objectives 了解: Recognize 线性微分方程组的一般理论； General theory of linear differential equations 理解: Understand 非齐线性微分方程组； Nonhomogeneous linear differential equation 掌握: Master 矩阵指数 expA 的定义和性质； Definition and properties of matrix exponent 德育目标 Moral Objectives 2-1 理解微分方程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 differential equation 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 非齐线性微分方程组； Nonhomogeneous linear differential equation 难点: Focal points 基解矩阵的计算公式。 Calculus formula of fundamental matrix 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 非线性微分方程 Nonlinear differential equations 知识点: Knowledge Delivery 解的稳定性概念； Definition of stability of solution 常微分方程组的存在唯一性定理； Existence of unique solution of ordinary differential equations 李雅普诺夫稳定性； Lyapunov stability 稳定、不稳定、渐近稳定的概念。 Definition of stability, instability, appropriate stability 学习目标: Learning Objectives 了解: Recognize 解的稳定性概念； Definition of stability of solution 理解: Understand 稳定、不稳定、渐近稳定的概念。 Definition of stability, instability, appropriate stability 掌握: Master 李雅普诺夫稳定性； Lyapunov stability 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 world2-4培养服务意识，具有“以人为本”的服务精神Cultivate serviceconsciousness and have theservice 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 bythelaw, understand andobey the rules重点：常微分方程组的存在唯一性定理；Key PointsExistence of unique solution of ordinary differential equations难点：李雅普诺夫稳定性：Focal pointsLyapunov stability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理论实验实践PBLEXP.PRACLECT.一阶微分方程的初等解法00018Fundamental solving method of the first orderdifferential equation一阶微分方程的解的存在定理6000Existencetheoremof solutionofthefirstorderdifferential equation高阶微分方程00012Higher order differential equation线性微分方程组14000Linear differential equations非线性微分方程6000Nonlineardifferential equations05600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 linesor revise content based on subject勾选Check教学方法与特色TeachingMethodology&Characters多媒体教学：基于信息化设备的课堂教学团Multi-media-basedlecturing团实践能力传授：理论与行业、实际案例相结合9/11

9 / 11 competitiveness in the area of the China engineering in the world. 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 重点: Key Points 常微分方程组的存在唯一性定理； Existence of unique solution of ordinary differential equations 难点: Focal points 李雅普诺夫稳定性； Lyapunov stability 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 一阶微分方程的初等解法 Fundamental solving method of the first order differential equation 18 0 0 0 一阶微分方程的解的存在定理 Existence theorem of solution of the first order differential equation 6 0 0 0 高阶微分方程 Higher order differential equation 12 0 0 0 线性微分方程组 Linear differential equations 14 0 0 0 非线性微分方程 Nonlinear differential equations 6 0 0 0 总计 Total 56 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 linesor revise content based on subject. 勾选 Check 教学方法与特色 Teaching Methodology & Characters  多媒体教学：基于信息化设备的课堂教学 Multi-media-basedlecturing  实践能力传授：理论与行业、实际案例相结合

Combining theorywith industrial practical problems课程思政建设：知识讲授与德育相结合团KnowledgedeliverywithethiceducationPBL教学：问题驱动的分组学习与交流口Problem-basedlearning其他：单击或点击此处输入文字。口Other:单击或点击此处输入文字。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 linesor revise content based on subject.考核环节：环节负责人：刘超平时BehaviorDirectorAssessment Content给分形式：课程总成绩比重(%):50百分制MarksResult TypePercentage (%)平时成绩，以学生平时课堂表现、课堂教师随机提问，学生平时作业完成情况综合评定，其中，学生平时课堂表现、课堂教师随机提问占比10%，学生平时作业（课前预习作业、课后作业)完成情况占考核方式：比90%MeasuresAccording to instant answer to the teacher's questions, comprehensivereport and question performance,themarkis evaluated, wherequestionperformance and instant answer accounts for 10%, assignmentsperformance(pre-lectureandpost-lecture)accountsfor90%.考核环节环节负责人：期末Final刘超DirectorAssessment Content给分形式课程总成绩比重(%):50百分制MarksResult TypePercentage (%)考试（提供重要数学公式），2小时答题及10分钟读题时间考核方式Examination(with some important mathematical equation sheet),twoMeasureshours andten minutes reading time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)改进措施：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Measures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。10/11

10 / 11 Combining theory with industrial practical problems  课程思政建设：知识讲授与德育相结合 Knowledgedeliverywithethiceducation ☐ PBL 教学：问题驱动的分组学习与交流 Problem-basedlearning ☐ 其他:单击或点击此处输入文字。 Other:单击或点击此处输入文字。 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 linesor revise content based on subject. 考核环节: Assessment Content 平时 Behavior 环节负责人: Director 刘超 给分形式: Result Type 百分制 Marks 课程总成绩比重(%): Percentage (%) 50 考核方式: Measures 平时成绩，以学生平时课堂表现、课堂教师随机提问，学生平时作 业完成情况综合评定，其中，学生平时课堂表现、课堂教师随机提 问占比 10%, 学生平时作业(课前预习作业、课后作业)完成情况占 比 90%. 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 期末 Final 环节负责人: Director 刘超 给分形式: Result Type 百分制 Marks 课程总成绩比重(%): Percentage (%) 50 考核方式: Measures 考试（提供重要数学公式），2 小时答题及 10 分钟读题时间 Examination(with some important mathematical equation sheet), two hours and ten minutes reading time. 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