线性代数I教学大纲

浏览次数：208

《线性代数》教学大纲

一、课程基本信息

开课单位:	数学科学研究所	课程代码:	SI131
课程名称:	线性代数	英文名称:	Linear Algebra
学分:	4	学时:	64
授课对象:		授课语言:	中英文
先修课程:

二、课程简介和教学目的

In this course, we will cover the following contents: Systems of linear equations, Gaussian elimination, matrices, determinants, and Cramer’s rule. Vectors, vector spaces, basis and dimension, linear transformations. Eigenvalues, eigenvectors, and quadratic forms.Objective:Solve and Interpret systems of linear equations.Understand the elementary facts of abstract vector space.Understand the linear transform

三、教学内容、教学方式和学时安排

课堂教学内容	教学进度和学时安排	教学方式
1 Introduction to Vectors 1.1 Vectors and Linear Combinations 1.2 Lengths and Dot Products 1.3 Matrices	第1周 4学时	课堂教学、课后复习（作业）、文献阅读、讨论
2 Solving Linear Equations 2.1 Vectors and Linear Equations 2.2 The Idea of Elimination 2.3 Elimination Using Matrices 2.4 Rules for Matrix Operations 2.5 Inverse Matrices 2.6 Factorization: A = LU 2.7 Transposes and Permutations	第二周第三周 8个学时	课堂教学、课后复习（作业）、文献阅读、讨论
3 Vector Spaces and Subspaces 3.1 Spaces of Vectors 3.2 The Nullspace of A: Solving Ax = 0 3.3 The Rank and the Row Reduced Form 3.4 The Complete Solution to Ax = b 3.5 Independence, Basis and Dimension 3.6 Dimensions of the Four Subspaces	第四周至第六周 12个学时	课堂教学、课后复习（作业）、文献阅读、讨论
4 Orthogonality 4.1 Orthogonality of the Four Subspaces 4.2 Projections 4.3 Least Squares Approximations 4.4 Orthogonal Bases and Gram-Schmidt	第七周第八周 8个学时	课堂教学、课后复习（作业）、文献阅读、讨论
Midterm exam	第九周 2个学时
5 Determinants 5.1 The Properties of Determinants 5.2 Permutations 5.3 Cramer's Rule, Inverses	第九周至第十周 6个学时	课堂教学、课后复习（作业）、文献阅读、讨论
6 Eigenvalues and Eigenvectors 6.1 Introduction to Eigenvalues 6.2 Diagonalizing a Matrix 6.3 Applications to Differential Equations 6.4 Symmetric Matrices 6.5 Positive Definite Matrices 6.6 Similar Matrices 6.7 Singular Value Decomposition (SVD)	第十一周第十三周 12个学时	课堂教学、课后复习（作业）、文献阅读、讨论
7 Linear Transformations 7.1 The Idea of a Linear Transformation 7.2 The Matrix of a Linear Transformation 7.3 Diagonalization and the Pseudoinverse	第十四周 4个学时	课堂教学、课后复习（作业）、文献阅读、讨论
讨论课	第十五周 4学时	复习、讨论
期末考试	第十六周 2学时	闭卷