No:
Syllabus
Course Name: Linear Algebra
Organization: CSIE
Grade: 2nd
Lecturer:
Foundation Course:
1.
■Required
Credit: 3
Algebra and Basic Math
□Elective
Hours:3
Teaching Objectives:
This course is to introduce the basic concept of linear algebra and it’s relative
principle and applications. The aim is to incubate student with the capabilities
of solving engineering problems using linear algebra and linear algebra and applying
linear algebra to engineering applications。
Course Objectives
Core Abilities
● Establish solid and professional
●1.1 Implement mathematic and logical abilities
abilities for students
○ 1.2 Have the specific abilities for information software
○ 1.3 Have the specific abilities for information hardware
◎ 1.4 Ability to explore, analyze, and solve unknown problems
● Develop abilities of information
● 2.1 Ability to employ modern software and understand the usage of
implementation and practice for students information systems
○ 2.2Ability to develop hardware and software for information systems
◎ Strengthen team works and
○ 3.1 Ability to communicate and cooperate with each other
cooperation for students in a wide range
◎ 3.2 Understanding of professional ethics and social responsibility
of learning
Symbols: ● Highly-Related ◎ Partially-Related ○ Non-Related
Outcomes and Assessment
This criterion assesses the quality and capabilities of the students and graduates. The program seeking accreditation
must:
1.1.1 ability to apply knowledge of mathematics, science, and engineering;
1.1.2 ability to carry out information process and scientific calculation;
2.1.1 ability to design and conduct experiments;
2.1.2 ability to analyze and interpret data;
2.2.1 ability to think logically, implement information technologies, and design creatively;
2.2.2 ability to analyze, design, and accomplish all kinds of problems by mean of independent thinking and integrated
creativity;
3.1.1 ability to apply professional techniques and make use of personal characteristics to provide practical contributions
for sake of self-establishment;
3.2.1 ability to organize, consult, and negotiate for solving professional problems via cooperating with a term in order to
be recognized by classmates and teachers;
3.3.1 ability to cultivate habits of life-long learning;
4.1.1 ability to care about society, humanities, enterprise ethics, and concern for society;
4.2.1 knowledge of contemporary issues; an understanding of the impact of engineering solutions in environmental,
societal, and global contexts in order to fit in with the changing impact of the international environment。
2.
Teaching Policy and Grading:

Teaching Policy: in class lecture, assignment, and programming in solving linear algebra
problems.

Grading Policy：Midterm exam：30%,Quiz and programming assignment：30%、Final: 40%
Descriptions for the Course:
Lecturing：A textbook will be selected as textbook for in-class lecturin。
Evaluation：Midterm exam,Quiz and programming assignment, and Final exam。
Teaching resources：Teaching material in PPT format will be uploaded to E-learning Website before
class。
Other items：Will be announced in E-learning Website。
3.
Contents and Progression:
Outline
Corresponding to Students’ Core
Implementation
Abilities
Topics
Contents
1. Introduction to Systems of
Linear Equations
System
of
Equations
Linear
2. Gaussian Elimination
3. Applications of Systems of
Linear Equations
● ● ○ ◎ ◎ ○ ○ ○ 
1. The Determinant of a Matrix
Determinants
2. Evaluation of a Determinant

● ● ○ ◎ ◎ ○ ○ ○ 
● ● ○ ◎ ◎ ○ ○ ○ 
● ● ○◎ ◎ ○ ◎ ○ 
4. Applications of Determinants ● ● ○ ◎ ◎ ○ ◎ ○
1. Vector Spaces
● ● ○ ◎ ◎ ○ ○ ○ 
2. Subspaces of Vector Spaces
● ● ○ ◎ ◎ ○ ○ ○ 
◎
● ● ○ ◎
◎ ○ ○ 
Independence
4. Basis and Dimension
● ● ○ ◎◎ ◎ ○ ○ 
5. Rank of a Matrix
● ● ○ ◎ ◎ ○ ○ ○ 
6. Coordinates and Change of
Basis
Inner Product Spaces
● ● ○ ◎ ◎ ○ ○ ○

3. Properties of Determinants
3. Spanning Sets and Linear
Vector Spaces
● ● ○ ○ ◎ ○ ○ ○
3. Elementary Matrices
Operations
C
● ● ○ ○ ◎ ○ ○ ○ 
2. The Inverse of a Matrix
4. Applications of Matrix
B
● ● ○ ○ ◎ ○ ○ ○ 
● ● ○ ◎ ◎ ○ ○ ○ 
● ● ○ ◎ ◎ ○ ○ ○ 
1. Matrix Operations
Matrices
1.1 1.2 1.3 1.4 2.1 2.2 3.1 3.2 A
1. Length and Dot Product
● ● ○ ◎ ◎ ○ ○ ○ 
● ● ○ ◎ ◎ ○ ○ ○ 


D
2. Inner Product Spaces
● ● ○ ◎ ◎ ○ ○ ○ 
3. Orthogonal Basis
● ● ○ ◎◎ ○ ○ ○ 
4. Least Square Analysis
1.
Introduction
to
Transformation
2. Kernel and Range
Linear Transformations 3.
Matrices
for
Transformations
4.
Transition
● ● ○ ◎◎ ◎ ○ ○ 
Linear
◎
● ● ○ ◎
○ ○ ○ 
● ● ○ ◎◎ ◎ ○ ○ 
Linear
◎
● ● ○ ◎
○ ○ ○ 
Matrices
and
Similarity
1. Eigenvalues and Eigenvectors
Eigenvalues
Eigenvectors
● ● ○ ◎
◎
◎ ○ ○ 
● ● ○ ◎◎ ◎ ○ ○ 
● ● ○ ◎◎ ◎ ○ ○ 
3. Symmetrical Matrices and
◎
● ● ○ ◎
◎ ○ ○ 
and 2. Diagonalization
Orthogonal Diagonalization
4.
References:
1. R. Larson, B.H. Edwards and D.C. Falvo, Elementary Linear Algebra, Houghton Mifflin, 2009. (Textbook)
2. H. Anton, Elementary Linear Algebra, Application version, 9th edition, John Wiley & Sons, Inc.,2005
3. WW. Cheney, D. Kincaid, Linear Algebra, Theory and Applications, Jones & Bartlett, 2009
4. Bretscher, Linear Algebra with Applications, 4th edition, Pearson, 2009
5. Linear algebra with application, Gareth Williams, 6th Ed., Jones and Bartlett Publishers, 2008