課程大綱及進度表

課程大綱及進度表

開課系所 Math

開課學年 99

開課學期 2

課程名稱(中文) 線性代數（一）

課程名稱（英文） LINEAR ALGEBRA(1)

課程碼 C111210

先修科目或先備能 力

高中數學

學分數 3

開課教師 粘珠鳳

e-mail [email protected]

電話 65146

Office Hours By Appointment 課程概述 1: Vectors Spaces

2: Linear Transformations and Matrices

3: Elementary Matrix Operations and Systems of Linear Equations 4: Determinants

教學目標 Introduction to basic topics and techniques in linear algebra.

授課課程大綱明細

Chapter 1 Vector Spaces

1.1 Introduction 1.2 Vector Spaces 1.3 Subspaces

1.4 Linear Combinations and Systems of Linear Equations 1.5 Linear Dependence and Linear Independence

1.6 Bases and Dimension

1.7* Maximal Linearly Independent Subsets

Chapter 2 Linear Transformations and Matrices

2.1 Linear Transformations, Null Spaces, and Ranges 2.2 The Matrix Representation of a Linear Transformation

2.3 Composition of Linear Transformations and Matrix Multiplication

2.4 Invertibility and Isomorphisms 2.5 The Change of Coordinate Matrix 2.6* Dual Spaces

Chapter 3 Elementary Matrix Operations and Systems of Linear

Equations

3.1 Elementary Matrix Operations and Elementary Matrices 3.2 The Rank of a Matrix and Matrix Inverses

3.3 Systems of Linear Equations---Theoretical Aspects 3.4 Systems of Linear Equations---Computational Aspects Chapter 4 Determinants

4.1 Determinants of Order 2 4.2 Determinants of order n 4.3 Properties of Determinants

4.4 Summary---Important Facts about Determinants 4.5* A Characterization of the Determinant

參考書目 Text book:

Linear Algebra, Fourth Edition

by S. Friedberg, A. Insel, and L. Spence

(See http://math.illinoisstate.edu/linalg/www.html ) Also, download free book at:

http://www.math.brown.edu/~treil/

by Sergei Treil (for reference).

課程要求

評量方式 Quiz and homework: 20%

2 midterms each counts for 25%

Final: 30%

課程網址 http://www.math.ncku.edu.tw/~cfnien/11SLinear.html 助教資訊

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