MATH 250 | Course Introduction and Application Information

Course Name
Linear Algebra and Differential Equations 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
Course Language
English
Course Type
Required
Course Level
First Cycle
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 and/or linear differential equations by providing them with the basic knowledge on linear vector spaces, matrix operations and linear differential equations , as well as on the methods for solving and analyzing linear systems of algebraic and differential equations.
Course Description The students who succeeded in this course;
  • will be able to determine if a linear system is consistent and solve the system by Gaussian elimination method
  • will be able to apply the basic techniques of matrix algebra, including finding the inverse of an invertible matrix using Gauss-Jordan elimination
  • will be able to apply basic concepts of linear models to various applications
  • will be able to find dimension and basis vectors of linear vector spaces and subspaces
  • will be able to find the eigenvalues and eigenvectors of a square matrix using the characteristic polynomial and diagonalize a matrix when this is possible
Course Content 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, solution methods for first order and second order ordinary differential equations and their engineering applications, eigenvalues eigenvectors analysis and diagonalization

 



Course Category

Core Courses
X
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. Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 1.1, 1.2
2 Row reduction and echelon forms, Vector equations, The matrix equation Ax=b. Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 1.2, 1.3, 1.4.
3 Solution sets of linear systems, Applications of Linear Systems. Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 1.5, 1.6
4 Linear Independence, Introduction to Linear Transformations. Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 1.7, 1.8
5 The matrix of a Linear Transformations, Linear Models in Business, Science and Engineering. Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 1.9, 1.10
6 Matrix Operations, Review for 1. MIDTERM Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 2.1
7 The inverse of a matrix, Characterization of invertible matrices, Matrix factorizations, Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 2.2, 2.3, 2.5
8 Introduction to determinants, Properties of determinants, Cramer’s rule, volume and linear transformations. Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 3.1, 3.2, 3.3
9 Vector spaces and subspaces, Null Spaces, Column Spaces and Linear Transformations Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 4.1, 4.2
10 Linearly Independent Sets, Bases, Application to Markov Chains. Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 4.3, 4.9
11 Eigenvalues and Eigenvectors, The Characteristic Equation. Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 5.1, 5.2
12 Review for 2. MIDTERM
13 Inner Product, Length, and Orthogonality, Orthogonal Sets. Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 6.1, 6.2
14 The Gram-Schmidt Process, Review. Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 6.3
15 Review
16 Review

 

Course Notes/Textbooks Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition.
Suggested Readings/Materials 1)Elementary Linear Algebra, Howard Anton, Chris Rorres, Wiley, 9th Edition. 2)Linear Algebra, Seymour Lipschutz, Shaum’s Outline Series, 2nd Edition.

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm
2
60
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
2
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
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
Study Hours Out of Class
16
3
Field Work
Quizzes / Studio Critiques
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
2
22
Final Exam
1
40
    Total
180

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

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

To have adequate knowledge in Mathematics, Science, Computer Science and Software Engineering; to be able to use theoretical and applied information in these areas on complex engineering problems.

X
2

To be able to identify, define, formulate, and solve complex Software Engineering problems; to be able to select and apply proper analysis and modeling methods for this purpose.

X
3

To be able to design, implement, verify, validate, document, measure and maintain a complex software system, process, or product under realistic constraints and conditions, in such a way as to meet the requirements; ability to apply modern methods for this purpose.

4

To be able to devise, select, and use modern techniques and tools needed for analysis and solution of complex problems in software engineering applications; to be able to use information technologies effectively.

5

To be able to design and conduct experiments, gather data, analyze and interpret results for investigating complex Software Engineering problems.

X
6

To be able to work effectively in Software Engineering disciplinary and multi-disciplinary teams; to be able to work individually.

7

To be able to communicate effectively in Turkish, both orally and in writing; to be able to author and comprehend written reports, to be able to prepare design and implementation reports, to be able to present effectively, to be able to give and receive clear and comprehensible instructions.

8

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

9

To be aware of ethical behavior, 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 Software Engineering, and to be able to communicate with colleagues in a foreign language.

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 Software Engineering.

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