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Linear Algebra

PÎRÎ REİS UNIVERSITY

ENGINEERING FACULTY

Electrical and Electronics Engineering Programme

2017 - 2018 Fall Term Course catalogue Form

 

Course Name : Linear Algebra

Degree: Undergraduate

 

Code

 

 

Year/Semester

 

Local Credits

 

ECTS Credits

 

Course Implementation, Hours/Week

Course

Tutorial

Laboratory

MATH113

1/1 (Fall)

2,5

4

2

1

0

Department

Electrical and Electronics Engineering

Instructors

Dr. Orhan Özgür AYBAR

Contact Information

oaybar@pirireis.edu.tr

Office Hours

TBA

Web page

www.pirireis.edu.tr

Course Type

 Compulsory

Course Language

English

Course Prerequisites

MATH 121

Course Category by Content %

Basic Sciences

Engineering Science

Engineering Design

Humanities

90

10

-

-

Course Description

Systems of linear equations, matrices, determinants, the Euclidean vector space, vector spaces and subspaces, eigen values and eigenvectors, diagonalization and quadratic forms, linear transformations

 

Course Objectives

 

  1. To introduce the fundamental concepts and methods of Linear Algebra
  2. To provide an ability to apply knowledge of linear algebra to solve engineering problems

 

Course Learning Outcomes

 

Upon successful completion of the course students should be able to:

  1. Find and classify the types of solutions of linear system of equations
  2. Perform basic matrix operations
  3. Use the row reduction operations put a matrix in upper echelon form
  4. Find the inverse of a matrix
  5. Compute the determinants of square matrices
  6. Understand and apply the basic properties of vectors in Rn
  7. Understand the concepts of vector space, basis, dimension and subspace.
  8. Determine the matrix representation of a linear transformation
  9. Find Eigen values and eigenvectors of a matrix
  10. Diagonalize a matrix and understand the concept of similarity of matrices

Instructional Methods and Techniques

Lecture, problem solving

Tutorial Place

Class

Co-term Condition

-

Textbook

H. Anton, C. Rorres, Elementary Linear Algebra, 10 th Edition, Wiley, 2010

Other References

B.Kolman, D.R.Hill, Elementary Linear Algebra with Applications, 9th Edition, Pearson, 2007

Homework & Projects

 

Laboratory Work

 

Computer Use

 

Other Activities

 

                   

 

Assessment Criteria

Activities

Quantity

Effects on Grading, %

Attendance

 

 

Midterm

1

30

Quiz

4

20

Homework

 

 

Term Paper/Project

 

 

Laboratory Work

 

 

Practices

 

 

Tutorial

 

 

Seminar

 

 

Presentation

 

 

Field Study

 

 

Final Exam

1

50

TOTAL

 

100

Effects of Midterm on Grading, %

 

50

Effects of Final on Grading, %

 

50

TOTAL

 

100

 

 

 

ECTS/ WORKLOAD TABLE

Activities

Count

Hours

Total Workload

Lecture

13

3

39

Midterm

1

20

20

Quiz

4

2

8

Homework

 

 

 

Term Paper/Project

 

 

 

Laboratory

 

 

 

Practices

 

 

 

Tutorial

 

 

 

Seminar

 

 

 

Presentation

 

 

 

Field Study

 

 

 

Final Exam

1

30

30

Total Workload

 

 

97

Total Workload/25

 

 

97/25

Course ECTS Credits

 

 

4

 

 

COURSE PLAN

 

 

Week

 

Topics

Course Outcomes

1

Introduction to Systems of  Linear Equations, Gaussian Elimination

I-II-III

 

2

Matrices and Matrix Operations, Inverses,  Algebraic Properties of Matrices

I-II-III-IV

 

3

Elementary Matrices and a Method for Finding A-1, More on Linear Systems  and Invertible Matrices, Diagonal, Triangular, and Symmetric Matrices

II-III-IV-V

 

4

Determinants by Cofactor Expansion, Evaluating Determinants by Row Reduction

VI

 

5

Properties of  Determinants,  Cramer’s Rule

VI-VII

 

6

Vectors in 2-Space, 3-Space, n-Space, Norm, Dot Product, and Distance in Rn, Orthogonality, The Geometry of Linear Systems, Cross Product

II-III-VIII

 

7

Real Vector Spaces, Subspaces, Linear Independence, Coordinates and Basis, Dimension

I-II-III

8

MIDTERM

 

 

9

Change of Basis, Row Space, Column Space, and Null Space, Rank, Nullity

VI

 

10

Eigenvalues and Eigenvectors, Diagonalization

II-III-IV

 

11

Orthogonal Matrices, Orthogonal Diagonalization, Quadratic Forms, Optimization Using Qudaratic Forms

II

 

12

Hermitian, Unitary, and Normal Matrices,  Linear Transformations, Isomorphism

II-IV-V

 

13

Compositions and Inverse Transformations

II-IV-VIII

 

14

Matrices for General Linear Transformations

II-IV-X

 

 

Relationship between the Course and the Electrical and Electronics Engineering Programme

Curriculum

 

 

 

Program Outcomes

Level of Contribution

1

2

3

a

An ability to apply knowledge of mathematics, science, and engineering

 

 

X

b

An  ability to design and conduct experiments, as well as to analyze and interpret data

 

X

 

c

An ability to design a system, component or process to meet desired needs

 

X

 

d

Ability to function on multi-disciplinary teams

 

X

 

e

An ability to identify, formulate, and solve engineering problems

X

 

 

f

An understanding of professional and ethical responsibility

X

 

 

g

An ability to communicate effectively

X

 

 

h

The broad education necessary to understand the impact of engineering solutions in a global and societal context

 

X

 

i

A recognition of the need for, and an ability to engage in life-long learning

X

 

 

j

A knowledge of contemporary issues

 

X

 

k

An ability to use the techniques, skills and modern engineering tools necessary for engineering practice

X

 

 

l

An ability to apply engineering knowledge in electric and electronics

 

X

 

 

         1: Small, 2: Partial, 3: Full

 

 

Programme Outcomes & Course Outcomes Connectivity Matrix

 

 

Course Outcomes

I

II

III

IV

V

VI

VII

VIII

IX

X

Programme Outcomes

a

 

 

X

X

X

X

X

X

 

 

b

 

X

 

 

X

X

X

 

 

 

c

 

X

 

 

 

 

 

 

 

 

d

 

X

 

X

 

 

 

X

 

 

e

X

 

 

 

X

X

X

 

X

X

f

X

 

 

 

 

 

 

 

 

 

g

X

 

 

X

 

 

 

 

 

 

h

 

X

 

 

 

X

 

 

 

 

i

X

 

X

 

 

 

X

 

 

 

j

 

X

 

 

X

 

X

X

 

X

k

X

 

 

X

 

 

 

 

 

 

l

 

X

 

 

X

 

X

X

X

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Prepared by

 

Date

 

Signature