Linear Algebra - 97 Academic Year

線性代數 - 97學年度

本課程是由 國立陽明交通大學工業工程與管理學系 提供。

本課程主要目的是說明線性代數之基本觀念及相關之定理與運算,使學習者建立運用線性代數解決有關工程與管理問題之基礎。

課程用書:
R. Larson, B.H. Edwards and D.C. Falvo, Elementary Linear Algebra, Houghton Mifflin, 2009.

為求學習成效完美,請購買課本!

授課教師 工業工程與管理學系 巫木誠老師
課程學分 3學分
授課年度 97學年度
授課對象 大學一年級學生
預備知識 
課程提供 課程影音   課程綱要   課程行事曆  

週次課程內容課程影音課程下載
1.1 Introduction to Systems of Linear Equations
1.2 Gaussian Elimination (1/2)
線上觀看MP4下載
1.1 Introduction to Systems of Linear Equations
1.2 Gaussian Elimination (2/2)
線上觀看MP4下載
1.3 Applications of Systems of Linear Equations
2.1 Operations with Matrices
2.2 Properties of Matrix Operations (1/2)
線上觀看MP4下載
1.3 Applications of Systems of Linear Equations
2.1 Operations with Matrices
2.2 Properties of Matrix Operations (2/2)
線上觀看MP4下載
2.3 The Inverse of a Matrix
2.4 Elementary Matrices
2.5 Applications of Matrix Operations (1/2)
線上觀看MP4下載
2.3 The Inverse of a Matrix
2.4 Elementary Matrices
2.5 Applications of Matrix Operations (2/2)
線上觀看MP4下載
3.1 The Determinant of a Matrix
3.2 Evaluation of a Determinant Using Elementary Operations
線上觀看MP4下載
3.3 Properties of Determinants
3.5 Applications of Determinants
4.1 Vectors in Rn
線上觀看MP4下載
Prelim Examination I (Ch1-Ch3)
(Exact date and time will be announced.)
4.2 Vector Spaces
線上觀看MP4下載
4.3 Subspaces of Vector Spaces
4.4 Spanning Sets and Linear Independence (1/2)
線上觀看MP4下載
4.3 Subspaces of Vector Spaces
4.4 Spanning Sets and Linear Independence (2/2)
線上觀看MP4下載
4.4 Spanning Sets and Linear Independence
4.5 Basis and Dimension (1/2)
線上觀看MP4下載
4.4 Spanning Sets and Linear Independence
4.5 Basis and Dimension (2/2)
線上觀看MP4下載
4.5 Basis and Dimension
4.6 Rank of a Matrix (1/2)
線上觀看MP4下載
4.5 Basis and Dimension
4.6 Rank of a Matrix (2/2)
線上觀看MP4下載
4.7 Coordinates and Change of Basis
5.1 Length and Dot Product (1/2)
線上觀看MP4下載
4.7 Coordinates and Change of Basis
5.1 Length and Dot Product (2/2)
線上觀看MP4下載
5.2 Inner Product Spaces
5.3 Orthogonal Basis (1/2)
線上觀看MP4下載
5.2 Inner Product Spaces
5.3 Orthogonal Basis (2/2)
線上觀看MP4下載
5.3 Orthogonal Basis
5.4 Least Square Analysis (1/2)
線上觀看MP4下載
5.3 Orthogonal Basis
5.4 Least Square Analysis (2/2)
線上觀看MP4下載
Prelim Examination II ( Ch4-Ch5) (Exact date and time will be announced.)
6.1 Introduction to Linear Transformation (1/2)
線上觀看MP4下載
Prelim Examination II ( Ch4-Ch5) (Exact date and time will be announced.)
6.1 Introduction to Linear Transformation (2/2)
線上觀看MP4下載
6.1 Introduction to Linear Transformation
6.2 Kernel and Range
線上觀看MP4下載
6.3 Matrices for Linear Transformations
6.4 Transition Matrices and Similarity (1/2)
線上觀看MP4下載
6.3 Matrices for Linear Transformations
6.4 Transition Matrices and Similarity (2/2)
線上觀看MP4下載
7.1 Eigenvalues and Eigenvectors
7.2 Diagonalization
線上觀看MP4下載
7.2 Diagonalization
7.3 Symmetrical Matrices and Orthogonal Diagonalization
線上觀看MP4下載

課程目標

本課程主要目的是說明線性代數之基本觀念及相關之定理與運算,使學習者建立運用線性代數解決有關工程與管理問題之基礎。

 

課程章節

章節 章節內容
System of Linear EquationsIntroduction to Systems of Linear Equations
Gaussian Elimination
Applications of Systems of Linear Equations 
MatricesMatrix Operations
The Inverse of a Matrix
Elementary Matrices
Applications of Matrix Operations 
Determinants The Determinant of a Matrix
Evaluation of a Determinant
Properties of Determinants
Applications of Determinants 
Vector SpacesVector Spaces
Subspaces of Vector Spaces
Spanning Sets and Linear Independence
Basis and Dimension
Rank of a Matrix
Coordinates and Change of Basis
Coordinates and Change of Basis
Inner Product SpacesLength and Dot Product
Inner Product Spaces
Orthogonal Basis
Least Square Analysis
Linear Transformations Introduction to Linear Transformation
Kernel and Range
Matrices for Linear Transformations
Transition Matrices and Similarity
Eigenvalues and EigenvectorsEigenvalues and Eigenvectors
Diagonalization
Symmetrical Matrices and Orthogonal Diagonalization

 

課程書目

R. Larson, B.H. Edwards and D.C. Falvo, Elementary Linear Algebra, Houghton Mifflin, 2009.

 

評分標準

項目百分比
每週小考25%
第一次期中考25%
第二次期中考25%
期末考25%

本課程行事曆提供課程進度與考試資訊參考。

學期週次
參考課程進度

第一週

  • 1.1 Introduction to Systems of Linear Equations
    1.2 Gaussian Elimination
第二週
  • 1.3 Applications of Systems of Linear Equations
    2.1 Operations with Matrices
    2.2 Properties of Matrix Operations
第三週
  • 2.3 The Inverse of a Matrix
    2.4 Elementary Matrices
    2.5 Applications of Matrix Operations
第四週
  • 3.1 The Determinant of a Matrix ;
    3.2 Evaluation of a Determinant Using Elementary Operations
第五週
  • 3.3 Properties of Determinants
    3.5 Applications of Determinants;
    4.1 Vectors in Rn
第六週
  • Prelim Examination I (Ch1-Ch3) (Exact date and time will be announced.)
    4.2 Vector Spaces;
第七週
  • 4.3 Subspaces of Vector Spaces;
    4.4 Spanning Sets and Linear Independence
第八週
  • 4.4 Spanning Sets and Linear Independence
    4.5 Basis and Dimension
第九週
  • 4.5 Basis and Dimension
    4.6 Rank of a Matrix
第十週
  • 4.7 Coordinates and Change of Basis
    5.1 Length and Dot Product
第十一週
  • 5.2 Inner Product Spaces
    5.3 Orthogonal Basis
第十二週
  • 5.3 Orthogonal Basis;
    5.4 Least Square Analysis
第十三週
  • Prelim Examination II ( Ch4-Ch5) (Exact date and time will be announced.)
    6.1 Introduction to Linear Transformation
第十四週
  • 6.1 Introduction to Linear Transformation;
    6.2 Kernel and Range
第十五週
  • 6.3 Matrices for Linear Transformations;
    6.4 Transition Matrices and Similarity
第十六週
  • 7.1 Eigenvalues and Eigenvectors;
    7.2 Diagonalization 
第十七週
  • 7.2 Diagonalization;
    7.3 Symmetrical Matrices and Orthogonal Diagonalization
第十八週
  • Final Examination (Ch6-Ch7) (Exact date and time will be announced)
PHP Code Snippets Powered By : XYZScripts.com