《Linear Algebra》课程教学大纲（三号黑体） 一、课程基本信息〈四号黑体) 英文名称 Linear Algebra 课程代码 课程性质 授课对象 New energy materials and devices (Chinese-foreign Cooperative) 学分 3 Credits 学 54 Hours 主讲教师 Jin-o Choi 修订日期 指定教材 D.C.Lay,(Linear Algebra and Its Applications)(Publishing House of Electronics Industry),2010. 二、课程目标（四号里体）"Linear Algebra"is a mathematica|course studving vector spaces and linear transformations.which are widely used in applied science and technology.The topics in the course will cover the fol lowing aspects:linear equations,vector equations and matrix equations,Iinear transformations.matrix operations,determinants.vector spaces.eigenvalues and eigenvectors. orthogonality.symmetric matrices and quadratic forms.etc.After learning the course.the students will develop the abilities to analyze and solve the practical problems related with linear algebra and vectors (一)总体目标：（小四号黑体 《以三目标知与技能、过程与方法。本与值的形式反隐接心养利内，其中核心素装不仅美注学生“当下罗”，美注学生 “未来发展”所需要的正确价值观名、必备品格和关健能力，即把知识、技能和过、方法提炼为能力，把情感态度、价值观提炼为品格)（五号米体） (二)课程目标：（小四号黑体） (课程目标规定某一阶段的学生通过课程学习以后，在发展德、智、体、美、芳等方面期银实现的程度。它是确定课程内容、教学目标和教学方法的基 础。)《五号宋体) :Master tris deterinant.space vector and other basic theories and basic knowledge through systematic learming Master the calculation of deterinant,the eleentary transformation of mtrix,the definition and calculation of trix rank,using the elenentary transfornation of matrix. Solving equations and inverse matrices.linear dependence of vector groups.eigenvalues and eigenvectors.ete. ions.quadratic form and linear transformation.can solve sone mathematical probleas 1.Ability to apply course content to research and analyze complex science and engineering probles. 2.To understand the general application of linear algebra in the energy industry.and closely related to the developnent of advanced materials science,enhance learning ability and learning awareness,enhance social responsibility. (三)课程目标与毕业要求、课程内容的对应关系（小四号黑体） 表1：课程目标与课程内容、毕业受求的对应关系表（五号宋体） 课程目标 躁程子目标 对应课程内容 对应毕业要求 课程目标1 Chapter ne Linear Equation 业要求 Chapter Two Matrix Algebra 工、材料 燕础知识、基本原理和基本实技能 Chapter Three Determinants
《Linear Algebra》课程教学大纲（三号黑体） 一、课程基本信息（四号黑体） 英文名称 Linear Algebra 课程代码 MDNE1025 课程性质 General education course 授课对象 New energy materials and devices （Chinese-foreign Cooperative） 学 分 3 Credits 学 时 54 Hours 主讲教师 Jin-Ho Choi 修订日期 指定教材 D. C. Lay，《Linear Algebra and Its Applications》, (Publishing House of Electronics Industry)，2010. 二、课程目标（四号黑体）"Linear Algebra" is a mathematical course studying vector spaces and linear transformations, which are widely used in applied science and technology. The topics in the course will cover the following aspects: linear equations, vector equations and matrix equations, linear transformations, matrix operations, determinants, vector spaces, eigenvalues and eigenvectors, orthogonality, symmetric matrices and quadratic forms, etc. After learning the course, the students will develop the abilities to analyze and solve the practical problems related with linear algebra and vectors. （一）总体目标：（小四号黑体） （以三维目标即知识与技能、过程与方法、情感态度与价值观的形式反映核心素养观念和内容，其中核心素养不仅关注学生“当下发展”，更关注学生 “未来发展”所需要的正确价值观念、必备品格和关键能力，即把知识、技能和过程、方法提炼为能力，把情感态度、价值观提炼为品格）（五号宋体） （二）课程目标：（小四号黑体） （课程目标规定某一阶段的学生通过课程学习以后，在发展德、智、体、美、劳等方面期望实现的程度，它是确定课程内容、教学目标和教学方法的基 础。）（五号宋体） 课程目标1：Master matrix, determinant, space vector and other basic theories and basic knowledge through systematic learning Master the calculation of determinant, the elementary transformation of matrix, the definition and calculation of matrix rank, using the elementary transformation of matrix. Solving equations and inverse matrices, linear dependence of vector groups, eigenvalues and eigenvectors, etc. 课程目标2：Through systematic study, master determinant calculation, matrix operation, elementary transformation, and apply to the solution of linear equations, quadratic form and linear transformation, can solve some mathematical problems. 1．Ability to apply course content to research and analyze complex science and engineering problems. 2. To understand the general application of linear algebra in the energy industry, and closely related to the development of advanced materials science, enhance learning ability and learning awareness, enhance social responsibility. （要求参照《普通高等学校本科专业类教学质量国家标准》，对应各类专业认证标准，注意对毕业要求支撑程度强弱的描述，与“课程目标对毕业要求 的支撑关系表一致）（五号宋体） （三）课程目标与毕业要求、课程内容的对应关系（小四号黑体） 表1：课程目标与课程内容、毕业要求的对应关系表 （五号宋体） 课程目标 课程子目标 对应课程内容 对应毕业要求 课程目标1 1.1 Chapter One Linear Equations Chapter Two Matrix Algebra Chapter Three Determinants 毕业要求1： 掌握新能源材料制备(或合成)、材料 加工、材料结构与性能测定等方面的 基础知识、基本原理和基本实验技能;
Chapter Four Vector Spaces Chapter Six Orthogonality Chapter Seven Symetric Vatrices and Quadratic Foras Chapter One Linear Equation 毕业要求2：能够应用数学、化学，物 Chapter Two Matrix Algebra 理等白然科学和工程科学的基本 Chapter Three Deterainants 理，识、表达并过文原究分日 1.2 Chapter Four Vector Spaces Chapter Five Elgenvalues and Eigenvectors 方法对复杂科 Chapter Six Orthogonality 通过信息综合符到合理有效的结论： atrices and Qdratic Chapter One Linear Equation 毕业要求：能够应用数学、化学、物 理等料学和工程料学的基本 Chapter Two Matrix Algebra 现，识别、表达并通过 做酹究分 Chapter Three Determinants 2.1 Chapter Four Yector Spaces hapter Five Eigenvaluesand Eigenvectors 通过信自修合料到合理有领的结论 Chapter Six Ortbogonality 账要求5：能够针对新作源复杂科 Chapter Seven Symetric Vatrices and Quadratic 问题，运用或开发适当的现代工具进行 文就检索、资料查询、分析等 误程目标阅 Chapter One Linear Equations Chapter Two Matrix Algebra 毕业婴求8：具有科学素养、社会责任 成，能够在士资中理解并道守职业过 德和规范，履行责任：9.能够在多学利 22 Chapter Four Vector Spaces 背景下的图队中承担个体、团队成员 Chapter Five Eigenvalues and Eigenvectors 以及负黄人的角色 Chapter Six Orthogonality ter Seven and Qudratic (大类基础课、专业教学课程及开放选修课程技照本科教学手册中各专业定的毕业要求填写“对应毕业要求“栏。通识教育课程含通识选修误程 三、教学内容（四号里体） (具体描送各章节教学目标、教学内容等。实验课程可按实验模块描透 第一章Linear Equations(小四号黑体) 1.教学目标（五号宋体） 2学重难点 Probleans: 1.Think of the relations aong linear equations and vector and matrix equations? 2.Think of the difference between linear dependence and linear independence?
Chapter Four Vector Spaces Chapter Five Eigenvalues and Eigenvectors Chapter Six Orthogonality Chapter Seven Symmetric Matrices and Quadratic Forms 1.2 Chapter One Linear Equations Chapter Two Matrix Algebra Chapter Three Determinants Chapter Four Vector Spaces Chapter Five Eigenvalues and Eigenvectors Chapter Six Orthogonality Chapter Seven Symmetric Matrices and Quadratic Forms 毕业要求2：能够应用数学、化学、物 理等自然科学和工程科学的基本原 理，识别、表达并通过文献研究分析 复杂科学工程问题，以获得有效结论; 毕业要求4：具备运用科学原理和科学 方法对复杂科学工程问题进行研究， 包括设计实验、分析和解释数据、并 通过信息综合得到合理有效的结论; 课程目标2 2.1 Chapter One Linear Equations Chapter Two Matrix Algebra Chapter Three Determinants Chapter Four Vector Spaces Chapter Five Eigenvalues and Eigenvectors Chapter Six Orthogonality Chapter Seven Symmetric Matrices and Quadratic Forms 毕业要求2：能够应用数学、化学、物 理等自然科学和工程科学的基本原 理，识别、表达并通过文献研究分析 复杂科学工程问题，以获得有效结论; 毕业要求4：具备运用科学原理和科学 方法对复杂科学工程问题进行研究， 包括设计实验、分析和解释数据、并 通过信息综合得到合理有效的结论; 毕业要求5：能够针对新能源复杂科学 问题,运用或开发适当的现代工具进行 文献检索、资料查询、分析等: 2.2 Chapter One Linear Equations Chapter Two Matrix Algebra Chapter Three Determinants Chapter Four Vector Spaces Chapter Five Eigenvalues and Eigenvectors Chapter Six Orthogonality Chapter Seven Symmetric Matrices and Quadratic Forms 毕业要求8：具有科学素养、社会责任 感，能够在实践中理解并遵守职业道 德和规范，履行责任;9.能够在多学科 背景下的团队中承担个体、团队成员 以及负责人的角色; 毕业要求12：具有自主学习和终身学 习的意识，有不断学习和适应发展的 能力。 （大类基础课程、专业教学课程及开放选修课程按照本科教学手册中各专业拟定的毕业要求填写“对应毕业要求”栏。通识教育课程含通识选修课程、 新生研讨课程及公共基础课程，面向专业为工科、师范、医学等有专业认证标准的专业，按照专业认证通用标准填写“对应毕业要求”栏；面向其他尚未有 专业认证标准的专业，按照本科教学手册中各专业拟定的毕业要求填写“对应毕业要求”栏。） 三、教学内容（四号黑体） （具体描述各章节教学目标、教学内容等。实验课程可按实验模块描述） 第一章 Linear Equations（小四号黑体） 1.教学目标 （五号宋体） Learning knowledges about linear equations. 2.教学重难点 Problems: 1. Think of the relations among linear equations and vector and matrix equations? 2. Think of the difference between linear dependence and linear independence?
sets of a general linear systeas? 3.教学内容 Section1:Introduction and Linear equations Class1:Introduction.Basic concepts of systes of linear eations Class 2:Row reduction and echelon fors Class3:Row reduction and echelon forms II.exercises Ca5iefintiootaTiCatioms,ercie Class 8:Solution sots of linear sxstems Section 3:Linear Independence and Linear Transformations Class 7:Definition of linear dependence and independenc Class 8:Introduction to linear transformations Class 9:The natrix of a linear transformation 4.教学方法 Nethod of lecture and questions between classes and tutoring after class 5.教学评价 Through the teaching of this chapter,students can aster linear eqations 第二章Matrix Algobra(小四号黑体) 1.教学日标（五号宋体） Learning knowledges about vector equations and matrix equations. 2教学重难 1.Think of the properties about matrix operations? 2.Think of the characterizations of invertible atrix? 3.What is a singular matrix? 4.What is the algoritha for finding the inverse of a matrix? 3.教学内容 Section I:Introduction to Natrix Operation Class 1:Definition of tri operations,addition,mltiplication,transpose Class 2:Inverse of a mtrix.erercises Class 3:Characterizations of invertibleatrix Section 2:More on natrix Class 4:Partitioned natris,exercises Class 5:Matrix equations,exercises 4.教学方法 Method of lecture and questions between classes and tutoring after class. 教学评价 Through the teaching of this chapter,students can aster vector equations eqution 第三章Determinants(小号黑体) 1.教学目标（五号宋体） Learning knowledges ahout deterninants.matrix operations and linear transformations 2教学重难点
3. What is row reduced echelon form? 4. What is a linear transformation? 5. Think of the solution sets of a general linear systems? 3.教学内容 Section 1: Introduction and Linear equations Class 1: Introduction, Basic concepts of systems of linear equations Class 2: Row reduction and echelon forms I Class 3: Row reduction and echelon forms II, exercises Section 2: Vector equations and matrix equations Class 4: Definition of vector equations, exercises Class 5: Definition of matrix equations, exercises Class 6: Solution sets of linear systems Section 3: Linear Independence and Linear Transformations Class 7: Definition of linear dependence and independence Class 8: Introduction to linear transformations Class 9: The matrix of a linear transformation 4.教学方法 Method of lecture and questions between classes and tutoring after class. 5.教学评价 Through the teaching of this chapter, students can master linear equations. 第二章 Matrix Algebra （小四号黑体） 1.教学目标 （五号宋体） Learning knowledges about vector equations and matrix equations. 2.教学重难点 Problems: 1. Think of the properties about matrix operations? 2. Think of the characterizations of invertible matrix? 3. What is a singular matrix? 4. What is the algorithm for finding the inverse of a matrix? 3.教学内容 Section 1: Introduction to Matrix Operations Class 1: Definition of matrix operations, addition, multiplication, transpose Class 2: Inverse of a matrix, exercises Class 3: Characterizations of invertible matrix Section 2: More on matrix Class 4: Partitioned matrix, exercises Class 5: Matrix equations, exercises Class 6: Elementary matrix, symmetric matrix, exercises 4.教学方法 Method of lecture and questions between classes and tutoring after class. 5.教学评价 Through the teaching of this chapter, students can master vector equations and matrix equations. 第三章 Determinants （小四号黑体） 1.教学目标 （五号宋体） Learning knowledges about determinants, matrix operations and linear transformations. 2.教学重难点 Problems:
1.hat is a determinant,how many ways to calculate it? What is a adjoint of a matrix? 3.教学内容 Section:Introdction to Deterins Class Class Froperties of determinants,exercises 4.教学方法 Nethod of lecture and questions between classes 5教学评价 Through the teaching of this chapter.students can sasterdeterminants.matrix operations and lipear transfornations 第四章V6 ctor Spa088(小四号黑体) 1.教学目标（五号宋体） 2教学重难点 Probleas: 1.What is a vector space and subspace? 2.Think of the difference between null space and column space? 3.What is the use of rank? 4.hat is the dimension of a vector space? 5.hat is the procedure fora change of basis and coordinate 3.教学内容 Section 1:Introduction to Vector Spaces Class 1:Definition of vector spaces and subspaces,properties Class 2:Definition of mll space,column space,exercises Class 3:Linearly independent sets.bases Class 7:Change of basis,exercises 4教学方法 Nethod of lecture and estios betseen classes and exercises after classes 5.教学评价 Through the teaching of this chapter,students can master vector spaces. 第五章Eigenvalues and Eigenvectors(小四号黑体) 1.教学目标（五号宋体 2.教学重难点 1.What are eigenvalues and eigenvectors? rop equ
1. What is a determinant, how many ways to calculate it? 2. Think of the relations between matrix and determinant? 3. What is a adjoint of a matrix? 4. What is the use of the Cramer’s rule? 5. What are general properties for determinant calculation? 3.教学内容 Section 1: Introduction to Determinants Class 1: Definition of determinants, the expansion theorem Class 2: Properties of determinants, exercises Class 3: Cramer’s rule, exercises Class 4: More calculation on determinants 4.教学方法 Method of lecture and questions between classes. 5.教学评价 Through the teaching of this chapter, students can masterdeterminants, matrix operations and linear transformations. 第四章 Vector Spaces（小四号黑体） 1.教学目标 （五号宋体） Learning knowledges about vector spaces. 2.教学重难点 Problems: 1. What is a vector space and subspace? 2. Think of the difference between null space and column space? 3. What is the use of rank? 4. What is the dimension of a vector space? 5. What is the procedure for a change of basis and coordinate transformation? 3.教学内容 Section 1: Introduction to Vector Spaces Class 1: Definition of vector spaces and subspaces, properties Class 2: Definition of null space, column space, exercises Class 3: Linearly independent sets, bases Section 2: Coordinate transformation Class 4: Definition of coordinate system, coordinate transformation Class 5: Dimension of a vector space, the basis theorem Class 6: Rank, the rank theorem, exercises Class 7: Change of basis, exercises 4.教学方法 Method of lecture and questions between classes and exercises after classes. 5.教学评价 Through the teaching of this chapter, students can master vector spaces. 第五章 Eigenvalues and Eigenvectors（小四号黑体） 1.教学目标 （五号宋体） Learning knowledges about eigenvalues and eigenvectors. 2.教学重难点 Problems: 1. What are eigenvalues and eigenvectors? 2. What is the procedure to solve eigen-problems? 3. What is the condition for a matrix which can be diagonalized or not? 4. What are the properties for the characteristic equation?
3教学内容 Section 1:Eigen-nrobleas Class 2:The characteristic eio exercises Class 3:Diagonalization of a matrix I Class 4:Diagonalization of a matrix II,exercises Class:Wore on eigeroe and diagonalization,exercises 4教学方法 Nethod of lecture and questloas between classes and exereises after classes 5.教学评价 Through the teaching of this chapter,students can ter earing koledges about eigenalues and eigevectors. 第六章0 rthogonality(小四号黑体) 1.教学目标（五号体） Learning knowledges about orthogoality. 2.教学重难点 3 What is the schuldt nrocess? 4.What is the use of orthogonal projcction? 5.Think of the difference between vector space and inmer product space? 3教学内容 Class:The Gran-Schaidt process,exercises Class 4:Inmer product spaces 4.教学方法 5教学评价 Through the teaching of this chapter,students can master orthogonality. 第七章Symetric Matrices and Quadratio Forms(小四号黑体) 1.教学目标（五号宋体） 2.教学重难点 at are the different tyes of auratie for 5.hat is the use of the principal axes theoren for quadratic forms? 3.教学内容 Class m Class3:Definition of guadratie for Class 4:The principal axes theoren,exercises
3.教学内容 Section 1: Eigen-problems Class 1: Definition of eigenvalues and eigenvectors Class 2: The characteristic equation, exercises Class 3: Diagonalization of a matrix I Class 4: Diagonalization of a matrix II, exercises Class 5: More on eigen-problems and diagonalization, exercises 4.教学方法 Method of lecture and questions between classes and exercises after classes. 5.教学评价 Through the teaching of this chapter, students can master Learning knowledges about eigenvalues and eigenvectors. 第六章 Orthogonality（小四号黑体） 1.教学目标 （五号宋体） Learning knowledges about orthogonality. 2.教学重难点 Problems: 1. What is inner product? 2. What is orthogonality? 3. What is the Schmidt process? 4. What is the use of orthogonal projection? 5. Think of the difference between vector space and inner product space? 3.教学内容 Section 1: Inner Product and Orthogonality Class 1: Definition of inner product, length, orthogonality Class 2: Orthogonal sets, orthogonal projection, exercises Class 3: The Gram-Schmidt process, exercises Class 4: Inner product spaces 4.教学方法 Method of lecture and questions between classes and exercises after classes. 5.教学评价 Through the teaching of this chapter, students can master orthogonality. 第七章 Symmetric Matrices and Quadratic Forms（小四号黑体） 1.教学目标 （五号宋体） Learning knowledges about symmetric matrices and quadratic forms, etc. 2.教学重难点 Problems: 1. Think of the difference in the diagonalization between common matrix and symmetric matrix? 2. What is the procedure for the diagonalization of a symmetric matrix? 3. What are the different types of quadratic forms? 4. What is the procedure for solving a quadratic form? 5. What is the use of the principal axes theorem for quadratic forms? 3.教学内容 Section 1: Symmetric matrices and quadratic forms Class 1: Diagonalization of symmetric matrix, exercises Class 2: The spectral theorem, exercises Class 3: Definition of quadratic form Class 4: The principal axes theorem, exercises
4教学方法 Method of e and questions bet lassesand after classes 5教学评价 Through the teaching of this chapter,students can sster symnetric rices and quadratic forus.ete. 四、学时分配（四号黑体） 表2：各章节的具体内容和学时分配表（五号宋体） 章背 章节内容 学时分配 第一章 Linear Equations 3 Weeks.9 Hours 第二章 Matrix Algebra 第三章 Determinants 2 Weeks,4 Hours 第四章 Vector Spaces 2 Weeks,7 Hours 第五章 Eigenvalues and Eigenvectors 2 Weeks,Hours 第六章 Orthogonality I Weeks,4 Hours 第七章 Sytric atrices and Quadratic Foras 五、教学进度（四号黑体） 表3：教学进度表（五号宋体） 周次 日期 章节名称 内容提要 授课时数 作业及要求 备注 1 930 hours inear equation 2-3 10.7&10.1 Linear Equations Vectorqiosand 6hours Master solving Linear 图trix equations equstions Introduction to Matrix 5 10.21 Matrix Algebra Operations and More on 6hours Understanding Linear 10.28 natrix equations 6-7 1L,4最 Determinants Introduction to 4 hours Understanding 11.1 Determinants Deterninants 89 Vector Spaces Master solving 10-11 122&129 Eigenvalues and Eigenvectors Eigen-problens 5hours Eigenvalues and Eigenvectors
4.教学方法 Method of lecture and questions between classes and exercises after classes. 5.教学评价 Through the teaching of this chapter, students can master symmetric matrices and quadratic forms, etc. 四、学时分配（四号黑体） 表2：各章节的具体内容和学时分配表（五号宋体） 章节 章节内容 学时分配 第一章 Linear Equations 3 Weeks，9 Hours 第二章 Matrix Algebra 2 Weeks，6 Hours 第三章 Determinants 2 Weeks，4 Hours 第四章 Vector Spaces 2 Weeks，7 Hours 第五章 Eigenvalues and Eigenvectors 2 Weeks，5 Hours 第六章 Orthogonality 1 Weeks，4 Hours 第七章 Symmetric Matrices and Quadratic Forms 1 Weeks，3 Hours 五、教学进度（四号黑体） 表3：教学进度表（五号宋体） 周次 日期 章节名称 内容提要 授课时数 作业及要求 备注 1 9.30 Linear Equations Introduction and Linear equations 3 hours Understanding Linear equations 2-3 10.7 &10.14 Linear Equations Vector equations and matrix equations 6 hours Master solving Linear equations 4-5 10.21 &10.28 Matrix Algebra Introduction to Matrix Operations and More on matrix 6 hours Understanding Linear equations 6-7 11.4 & 11.11 Determinants Introduction to Determinants 4 hours Understanding Determinants 8-9 11.18 & 11.25 Vector Spaces Introduction to Vector Spaces and Coordinate transformation 7 hours Master what is Vector Spaces 10-11 12.2 & 12.9 Eigenvalues and Eigenvectors Eigen-problems 5 hours Master solving Eigenvalues and Eigenvectors
12.16 Orthogonnlity Inner Product and 4 hours Understanding Orthogonality Orthogonality Master Symnetric 13 12.23 Symetric Natrices and Symmetric natrices and Quadratic Forms quadratie foras 3 hours Matrices and Quadratic 六、教材及参考书目（四号黑体） 《电子学术资源、纸顺学术资源等，按规范方式列举)（五号末体） Textbooks:D.C.Lay.(Linear Algebra and Its Applicaticns)(Publishing House of Electronics Industry).2010. References 1.Linear Algebra,by Z..Tang.et al..(Science Press,2011).(In Chinese 2 Linear Al gebra rsity,(Higher Educa ed).by L.. e55.2012 5.Linear Algebra done right (2ed),by S.Axler,Beijing orld Publishing Corporation.2008) 七、教学方法《四号黑体) (讲授法、时论法、案例教学法等，按规范方式列举，并进行简要说明)（五号宋体） Theoretical class teaching. practice and discussion class and problen coamnication, electronic resources and mathemtics experiment learning guidance 八、考核方式及评定方法（四号黑体） (一)课程考核与课程目标的对应关系《小四号黑体) 表4：课程考核与课程目标的对应关系表（五号宋体 误程目标 考要点 考方式 课程目标 Learning knowledges about linear equations QA.quiz in class 课程目起 .quiz in class 课程目标3 QtA.quiz im class 课程目标 kovledges about vector spaces. QA.quiz in class 误程目标 Learning knoledges ahout eigenvaluesand Q4A.quiz in class eigenvectors. 课程目标6 QA.quiz in class 课程目标 QtA.quiz in class rati forms,etc
12 12.16 Orthogonality Inner Product and Orthogonality 4 hours Understanding Orthogonality 13 12.23 Symmetric Matrices and Quadratic Forms Symmetric matrices and quadratic forms 3 hours Master Symmetric Matrices and Quadratic Forms 六、教材及参考书目（四号黑体） （电子学术资源、纸质学术资源等，按规范方式列举）（五号宋体） Textbooks：D. C. Lay，《Linear Algebra and Its Applications》，(Publishing House of Electronics Industry)，2010. References： 1. Linear Algebra, by Z.M. Tang, et al., (Science Press, 2011). (In Chinese) 2. Linear Algebra (6ed), by Tongji University, (Higher Education Press, 2014). (In Chinese) 3. Linear Algebra with Applications (9ed), by S.J. Leon, (China Machine Press, 2017). 4. Introduction to Linear Algebra (5ed), by L.W. Johnson, et al., (China Machine Press, 2012). 5. Linear Algebra done right (2ed), by S. Axler, (Beijing World Publishing Corporation, 2008). 七、教学方法 （四号黑体） （讲授法、讨论法、案例教学法等，按规范方式列举，并进行简要说明）（五号宋体） Theoretical class teaching, practice and discussion class, Q&A and problem communication, electronic resources and mathematics experiment learning guidance. 八、考核方式及评定方法（四号黑体） （一）课程考核与课程目标的对应关系 （小四号黑体） 表4：课程考核与课程目标的对应关系表（五号宋体） 课程目标 考核要点 考核方式 课程目标1 Learning knowledges about linear equations. Q&A, quiz in class 课程目标2 Learning knowledges about vector equations and matrix equations. Q&A, quiz in class 课程目标3 Learning knowledges about determinants, matrix operations and linear transformations. Q&A, quiz in class 课程目标4 Learning knowledges about vector spaces. Q&A, quiz in class 课程目标5 Learning knowledges about eigenvalues and eigenvectors. Q&A, quiz in class 课程目标6 Learning knowledges about orthogonality. Q&A, quiz in class 课程目标7 Learning knowledges about symmetric matrices and quadratic forms, etc. Q&A, quiz in class
(二)评定方法（小四号黑体） 1.评定方法（五号宋体） (例：平时成镜：10期中考试：3%，期末考试60%，按课程考核实际情况述)（五号宋体 Course Attendance and Performance:10% Hogework and Quiz:206 Midterm Exam:30% Final Exan:40% 2。程目标的考核占比与达成度分析 (五号宋体) 表5：误程目标的考核占比与达成度分析表（五号宋体） 考核占比 期中 深程目标 期术 总评达成度 课程目标 20M 30m 0m 果程日标达成度-0.2x平时日标战+0.3x明中目 课程目标2 20% 50m 标成镜+05x期末目标成/目标总分。按课程考 实际情况描述 课程目标3 50N (三)评分标准（小四号黑体）】 评分标准 课 90-100 80-89 70-79 60-69 <60 良 中 合解 不合格 B c 0 课程 熟结掌探线性代数基理论 校熟练蒙症线性代数基础理 基本享控线性代数基础理 未全面蒙症线性代数基 未潭提线性代数基础理 目标1 与基知识 论与基础知识 论与基知识 过理论与基础知识 论与基础知识 只有的发性代 课程 而为学习后推速乃进一 而为学习后继速程及进一步 力，从而为学习后继课程 的能力，从而为学 目标 乃进先扩大识而 后维课程及进一步打大 后课程及进一步扩大 扩大知识面蓝定必更的勤 扩大知面菌定必亚的粉学 初识面道定以亚的数学 识面定必亚的酸学 必要的数学基础，并能龄 基础，并能第以此为工月分 基陆，并乳以此为工月 基础，并的以此为 础，并的够以此为 以此为工只分析和处理工 析和处理工程实标问题， 析和理工程实际问题。 程实际问题， 具分析和处理工程实际 具分桥和处理工程实际 。 具有自主学习和终身学习的 具有自主学习和终身学习的 具有自主学习和终身学习 且右白卡学习们终身学 且右白主学习和终身学 意识，有不断学习和适应发 意识。有不断学习和话应发 的意识，有不断学习和证 习的意识，有不新学习 习的意识，有不断学习 目标3 展的能力。 展的能力。 应发展的能力。 和适应发展的能力， 和适应发展的能力
（二）评定方法 （小四号黑体） 1．评定方法 （五号宋体） （例：平时成绩：10%，期中考试：30%，期末考试60%，按课程考核实际情况描述）（五号宋体） Course Attendance and Performance: 10% Homework and Quiz: 20% Midterm Exam: 30% Final Exam: 40% 2．课程目标的考核占比与达成度分析 （五号宋体） 表5：课程目标的考核占比与达成度分析表（五号宋体） 考核占比 课程目标 平时 期中 期末 总评达成度 课程目标1 20% 30% 50% 课程目标达成度={0.2ｘ平时目标成绩+0.3ｘ期中目 标成绩+0.5ｘ期末目标成绩}/目标总分。按课程考 核实际情况描述 课程目标2 20% 30% 50% 课程目标3 20% 30% 50% （三）评分标准 （小四号黑体） 课程 目标 评分标准 90-100 80-89 70-79 60-69 ＜60 优 良 中 合格 不合格 A B C D F 课程 目标1 熟练掌握线性代数基础理论 与基础知识 较熟练掌握线性代数基础理 论与基础知识 基本掌握线性代数基础理 论与基础知识 未全面掌握线性代数基 础理论与基础知识 未掌握线性代数基础理 论与基础知识 课程 目标2 具有熟练的线性代数运算能 力，能利用线性代数方法解 决一些实际问题的能力，从 而为学习后继课程及进一步 扩大知识面奠定必要的数学 基础，并能够以此为工具分 析和处理工程实际问题。 具有熟练的线性代数运算能 力，能利用线性代数方法解 决一些实际问题的能力，从 而为学习后继课程及进一步 扩大知识面奠定必要的数学 基础，并能够以此为工具分 析和处理工程实际问题。 具有熟练的线性代数运算 能力，能利用线性代数方 法解决一些实际问题的能 力，从而为学习后继课程 及进一步扩大知识面奠定 必要的数学基础，并能够 以此为工具分析和处理工 程实际问题。 具有熟练的线性代数运 算能力，能利用线性代 数方法解决一些实际问 题的能力，从而为学习 后继课程及进一步扩大 知识面奠定必要的数学 基础，并能够以此为工 具分析和处理工程实际 问题。 具有熟练的线性代数运 算能力，能利用线性代 数方法解决一些实际问 题的能力，从而为学习 后继课程及进一步扩大 知识面奠定必要的数学 基础，并能够以此为工 具分析和处理工程实际 问题。 课程 目标3 具有自主学习和终身学习的 意识，有不断学习和适应发 展的能力。 具有自主学习和终身学习的 意识，有不断学习和适应发 展的能力。 具有自主学习和终身学习 的意识，有不断学习和适 应发展的能力。 具有自主学习和终身学 习的意识，有不断学习 和适应发展的能力。 具有自主学习和终身学 习的意识，有不断学习 和适应发展的能力
