線性代數(shù)2教學(xué)大綱（英文版）

1、Syllabus of Linear Algebra IICourse Name: linear algebra II Course Code： Credits： 2 Total Credit Hours：32 Lecture Hours： 32 Experiment Hours： 0 Programming Hours：0 Practice Hours：0Total Number of Experimental (Programming) Projects 0 , Where, Compulsory ( 0 ), Optional ( 0 ).School： School of Scienc

2、e Target Major：biological engineering, food science and engineering, chemistry engineering, medicine and business、Course Nature & Aims This course is designed for those students with majors in biological engineering, food science and engineering, chemistry engineering, medicine and business major. T

3、his is a theoretic course. The aims of this course is to help students to grasp the basic theory concerning linear algebra, develop their ability in computing, thinking based on abstract concepts, reasoning by logical, and modeling by linear algebra. 、Course Objectives 1. Moral Education and Charact

4、er Cultivation. By this course, the students will learn basic theory and applications of linear algebra, they will get a comprehensive understanding to the methods and ideas of linear algebra, and develop the ability of using linear algebra to solve some practical problem from engineering and social

5、 science. By the introduction of some background of the concepts and examples concerning the application of linear algebra, the students will develop lots of good habits such as thinking like a scientist, working with hard will, solving problems creatively, etc. By this course, the students will kno

6、w some famous works of Chinese ancient mathematicians. 2. Course Objectives Through the study of this course, students qualities, skills, knowledge and abilities obtained are as follows：Objective 1. By this course, students will learn the basic knowledge and develop basic calculation skills about li

7、near algebra.（Corresponding to Chapter1-4, supporting for graduation requirements index 2,3）Objective 2. This course will help students to develop ability in abstract thinking, HYPERLINK javascript:; spacial HYPERLINK javascript:; imagination and logical reasoning.（Corresponding to Chapter 1-4, supp

8、orting for graduation requirements index 2,3）Objective 3. This course will help students to develop some skills of using what they learn in this course to solve some problems from different fields.（Corresponding to Chapter 1-4 , supporting for graduation requirements index 2,3）3. Supporting for Grad

9、uation RequirementsThe graduation requirements supported by course objectives are mainly reflected in the graduation requirements indices 2,3, as follows:Supporting for Graduation RequirementsCourse ObjectivesGraduation RequirementsIndices and Contents Supporting for Graduation RequirementsTeaching

10、TopicsLevel of Support IndicesContentsObjective 1Grasp special knowledge for majorIndex 2Can grasp all the mathematical knowledge that will be used in major coursesChapter 1-4HObjective 2,3Grasp special methods for research and solving special problemsIndex 3Can use mathematical theory and methods t

11、o solve related problems in HYPERLINK javascript:; professional HYPERLINK javascript:; fieldChapter1-4M、Basic Course ContentChapter 1 Matrices and Linear equations (supporting course objectives 1,2,3)Definition of matricesInverse matrices and determinantsProperties and calculations of determinantsEl

12、ementary transformations of matricesRank of matrix and Linear equationsBlock matrices*Examples of matrix applicationsTeaching Requirements: Through the teaching of this chapter, learn the basic theory of matrix, determinant and linear equations. Students are required to understand the concept of mat

13、rix and master the operations of matrix; understand the inductive definition of n-order determinants, and be able to skillfully use the properties of determinants and Cramers rule; understand the concept of inverse matrices and master the method of seeking inverse matrices with adjoint matrices ; un

14、derstand the operation of block matrix; understand and master the elementary transformation of matrix and its relationship with matrix multiplication; understand the concept and application of matrix rank; master the method of seeking the rank and the inverse of a matrix and solving linear equations

15、 with elementary transformation. Through learning, students should have more proficient computing skills and abstract thinking skills.Key Points: properties of determinants and their applications, matrixs operations and elementary transformations, and the rank of matrix and its applicationsDifficult

16、 Points：Comprehensive use of matrix and determinant theory to solve linear equationsChapter 2 Vectors and Linear equations (supporting course objectives 1,2,3)2.1 Vector groups and their linearly dependent2.2 Vector space2.3 Structure of the solution of linear equations2.4 *ApplicationsTeaching Requ

17、irements: Through the teaching of this chapter, learn the basic theory of vector space and its application in linear equations. Students are required to understand and master the linear operation of vectors; understand the concepts of linearly dependent and linearly independent of vector groups, and

18、 understand the relevant important conclusions; understand the concepts of maximal linearly independent family of a collection of vectors and the rank of vector group; use the elementary transformation method to seek the rank of the vector group and the maximal linearly independent family; understan

19、d and master the related concepts of the solution of the linear equations such as solution, general solution, special solution, basic solution system, etc., master the method of using the vector space theory to study the linear equations and its solution space . Through learning, students should hav

20、e more proficient computing ability, reasoning ability, abstract thinking ability and preliminary ability to solve problems by applying theory.Key Points：Linearly dependent, vector space and the solution space of linear equationsDifficult Points：Linearly dependent, and the solution space of linear e

21、quationsChapter 3 Linear transformation and similar matrices (supporting course objectives 1,2,3)3.1* Base transformation and coordinate transformation3.2* Linear transformation3.3 Similar matrices3.4 Similarity diagonalization of matrices3.5 Orthogonal matrix and orthogonal transformation3.6 *Simpl

22、e application about similarity diagonalization of matricesTeaching Requirements: Through the teaching of this chapter, learn the basic concepts of basis, coordinates, transition matrix, matrix representation of linear transformation, similar matrix, eigenvalues, eigenvectors, similarity diagonalizat

23、ion, orthogonal transformation and so on. Students are required to understand base transformation and coordinate transformation, understand the matrix of linear transformation, understand the background of similar matrix; grasp the definition of similar matrix; understand the concept of matrix eigen

24、values and eigenvectors and master their methods; understand the concepts and properties of orthogonal matrix and orthogonal transformation; understand the conditions of matrix diagonalization and master the method of matrix diagonalization. Through learning, students should have more proficient com

25、puting ability, reasoning ability, abstract thinking ability and preliminary ability to solve problems by applying theory.Key Points：Similar matrices and the method of similarity diagonalizationDifficult Points：the concept and background of matrix similarityChapter 4 Quadratic forms and normal forms

26、 (supporting course objectives 1,2,3)4.1 Quadratic forms and normal forms4.2 Positive definite quadratic form4.3* Simple applications of quadratic form theoryTeaching Requirements: Through the teaching of this chapter, learn the basic theory of quadratic form, such as quadratic form, matrix of quadr

27、atic form, normal form, positive definite quadratic form, etc. Understand the background of the quadratic form and its matrix representation; will use the orthogonal transformation method to transform the quadratic form into the normal form, understand how to obtain the normal forms by using matchin

28、g method, know the rank of the quadratic form, the positive definiteness of the quadratic form and its discriminant method. Through learning, students should have more proficient computing ability, reasoning ability, abstract thinking ability and preliminary ability to solve problems by applying the

29、ory.Key Points：the method of transform the quadratic form into the normal form, judgment of positive definiteness of quadratic formDifficult Points：the method of transform the quadratic form into the normal form、Table of Credit Hour Distribution Teaching ContentIdeological and Political Integrated L

30、ecture HoursExperiment HoursPractice HoursProgramming HoursSelf-study HoursExercise ClassDiscussion HoursChapter1Scientific spirit, ancient Chinese mathematics achievements102Chapter2Scientific spirit62Chapter3Scientific spirit62Chapter4Scientific spirit22Total248Sum32、Summary of Experimental (Progr

31、amming) Projects No、Teaching Method Lectures delivered by teachers in the classroom.、Course Assessment and Achievement Evaluation Assessment Methods：Examination Examination Formats: Closed-bookGrading Methods：Hundred-mark SystemCourse Assessment Content, Assessment Format and Supporting Course Objec

32、tivesCourse Objectives（Indices）Assessment ContentAssessment Formats and Proportion（）GradingClassroom QuestioningAssignment EvaluationRoutineTestExperiment ReportTermReportTermPaperMidterm ExamFinal ExamProportion（）Objective 1（Index 2,3）Matrix, Determinant, Linear equations, Vector spaceSimilar matrix, Quadratic form202060100Objective 2（Index 2,3）Matrix, Determinant