FACULTY OF ENGINEERING

Department of Aerospace Engineering

MATH 250 | Course Introduction and Application Information

Course Name
Linear Algebra for Engineers
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 250
Fall
3
0
3
6

Prerequisites
  MATH 153 To get a grade of at least FD
or MATH 109 To get a grade of at least FD
Course Language
English
Course Type
Required
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course Problem Solving
Q&A
Lecture / Presentation
Course Coordinator
Course Lecturer(s)
Assistant(s)
Course Objectives The main objective of this course is to establish a basic mathematical background for the students who will receive engineering courses based on linear algebra by providing them with the basic knowledge on linear vector spaces, matrix operations as well as on the methods for solving and analyzing linear systems of algebraic equations.
Learning Outcomes The students who succeeded in this course;
  • apply the row operations to find (reduced) row echelon forms of matrices.
  • find the inverse of a matrix.
  • apply basic concepts of linear models to various applications.
  • evaluate the determinants of matrices.
  • investigate the linear independence of vectors.
  • identify vector spaces and their subspaces.
  • compute the eigenvalues of a matrix and corresponding eigenvectors.
  • describe the inner product.
Course Description The main subjects of the course are the vector and matrix operations, linear independence and dependence of vectors, linear vector spaces and subspaces, dimensions and basis vectors for vector spaces, linear transformations, determinants, eigenvalue and eigenvectors.

 



Course Category

Core Courses
Major Area Courses
Supportive Courses
Media and Management Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Systems of linear equations, row reduction and echelon forms, vector equations David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.1, 1.2, D0avid C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.1, 1.2, 1.3
2 The matrix equation Ax=b, Solution sets of linear systems, applications of linear systems David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.4, 1.5, 1.6
3 Linear Independence, introduction to linear transformations David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.7, 1.8
4 The matrix of a linear transformations, linear models in business, science and engineering David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.9, 1.10
5 Matrix operations, The inverse of a matrix David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 2.1, 2.2
6 Characterization of invertible matrices, Matrix factorizations David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 2.3, 2.5
7 Midterm
8 Introduction to determinants, properties of determinants, David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015).Section 3.1, 3.2, 3.3
9 Cramer’s rule, volume, and linear transformations, Vector spaces and subspaces David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015).Section 3.3, 4.1
10 Null spaces, column spaces, and linear transformations, Linearly independent sets, bases David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 4.2, 4.3
11 The dimension of a vector space, Rank, Application for Markov chains David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 4.5, 4.6, 4.9
12 Eigenvalues and eigenvectors, The characteristic equation, Diagonalization David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 5.1, 5.2, 5.3
13 Diagonalization, Inner product, length, and orthogonality, orthogonal sets David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 5.3, 6.1, 6.2
14 The Gram-Schmidt process, review David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Section 6.4
15 Semester review
16 Final exam

 

Course Notes/Textbooks

David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed. (Pearson,

2015). ISBN-13:978-0321982384

Suggested Readings/Materials

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
5
20
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm
1
30
Final Exam
1
50
Total

Weighting of Semester Activities on the Final Grade
6
50
Weighting of End-of-Semester Activities on the Final Grade
1
50
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Theoretical Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: '.16.' x total hours)
16
0
Study Hours Out of Class
14
3
42
Field Work
0
Quizzes / Studio Critiques
5
6
30
Portfolio
0
Homework / Assignments
0
Presentation / Jury
0
Project
0
Seminar / Workshop
0
Oral Exam
0
Midterms
1
28
28
Final Exam
1
32
32
    Total
180

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To have theoretical and practical knowledge that have been acquired in the area of Mathematics, Natural Sciences, and Aerospace Engineering.

X
2

To be able to assess, analyze and solve problems by using the scientific methods in the area of Aerospace Engineering.

3

To be able to design a complex system, process or product under realistic limitations and requirements by using modern design techniques.

4

To be able to develop, select and use novel tools and techniques required in the area of Aerospace Engineering.

X
5

To be able to design and conduct experiments, gather data, analyze and interpret results.

6

To be able to develop communication skills, ad working ability in multidisciplinary teams.

7

To be able to communicate effectively in verbal and written Turkish; writing and understanding reports, preparing design and production reports, making effective presentations, giving and receiving clear and understandable instructions.

8

To have knowledge about global and social impact of engineering practices on health, environment, and safety; to have knowledge about contemporary issues as they pertain to engineering; to be aware of the legal ramifications of Aerospace Engineering solutions.

9

To be aware of professional and ethical responsibility; to have knowledge about standards utilized in engineering applications.

10

To have knowledge about industrial practices such as project management, risk management, and change management; to have awareness of entrepreneurship and innovation; to have knowledge about sustainable development.

11

To be able to collect data in the area of Aerospace Engineering, and to be able to communicate with colleagues in a foreign language (‘‘European Language Portfolio Global Scale’’, Level B1).

12

To be able to speak a second foreign language at a medium level of fluency efficiently.

13

To recognize the need for lifelong learning; to be able to access information, to be able to stay current with developments in science and technology; to be able to relate the knowledge accumulated throughout the human history to Aerospace Engineering.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 


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