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

Mechanical 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

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

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 basic knowledge in fluid mechanics, structural mechanics, material properties, and energy/propulsion systems in the context of mechanical engineering design

X

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

Course Name : Linear Algebra

Degree: Bachelor

Code

Year/Semester

Local Credits

ECTS Credits

Course Implementation, Hours/Week

Course

Tutorial

Laboratory

MATH113

1/1 (Fall)

2.5

4

2

1

Department

Naval Architecture and Marine Engineering

Mechanical Enginering

Electrical and Electronics Engineering

Industrial Engineering

Instructors

Assist. Prof. Dr. Orhan Özgür Aybar

Contact Information

Piri Reis University, Faculty of Arts and Sciences Tuzla-Istanbul

Phone: +90 216 5810050

E-mail: oaybar@pirireis.edu.tr

Office Hours

Web page

http://www.pirireis.edu.tr/pruonline/www/index.php

Course Type

 Compulsory

Course Language

English

Course Prerequisites

  None

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, eigenvalues and eigenvectors, diagonalization and quadratic forms, linear transformations

Course Objectives

This course is designed for engineering students

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 reprerentation of a linear transformation
9. Find eigenvalues 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

Co-term Condition

Textbook

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

Other References

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

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%

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

8

MIDTERM

II-IV

9

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

IV

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

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 legal, societal and environmental knowlegde in maritime transport and in all respective modes of transport operations.

X

m

An ability to interpret and analysis of the data regarding maritime management and operations, recognition and solution of problems for decision making process.

X

Prepared by

Date

Signature