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
Spring
3
0
3
6

Prerequisites
None
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.
Learning Outcomes 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
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 Models in Business, Science and Engineering, Matrix Operations 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, The inverse of a matrix, Characterization of invertible matrices. Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 2.1, 2.2, 2.3
7 Review
8 Matrix factorizations, Introduction to determinants, Properties of determinants. Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 2.5, 3.1 3.2
9 Cramer’s rule, volume and linear transformations, Vector spaces and subspaces. Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 3.3, 4.1
10 Null Spaces, Column Spaces and Linear Transformations, Linearly Independent Sets, Bases. Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 4.2, 4.3.
11 Application to Markov Chains, Eigenvalues and Eigenvectors. Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 4.9, 5.1.
12 The Characteristic Equation, Inner Product, Length, and Orthogonality Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 5.2, 6.1.
13 Orthogonal Sets, The Gram-Schmidt Process Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition, Section 6.2, 6.4
14 Review
15 Review
16 Review

 

Course Textbooks Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson, 5th Edition.
References 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 Requirements Number Percentage
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
4
20
Homework / Assignments
8
10
Presentation / Jury
Project
Seminar / Workshop
Portfolios
Midterms / Oral Exams
1
30
Final / Oral Exam
1
40
Total

Contribution of Semester Work to Final Grade
13
60
Contribution of Final Work to Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Activities Number Duration (Hours) Workload
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
4
3
Homework / Assignments
8
2
Presentation / Jury
Project
Seminar / Workshop
Portfolios
Midterms / Oral Exams
1
22
Final / Oral Exam
1
34
    Total
180

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

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

To have sufficient background in Mathematics, Basic sciences and Biomedical Engineering areas and the skill to use this theoretical and practical background in the problems of the Biomedical Engineering.

2

To identify, formulate and solve Biomedical Engineering-related problems by using state-of-the-art methods, techniques and equipment; to select and apply appropriate analysis and modeling methods for this purpose.

3

To analyze a complex system, system components or process, and to design with realistic limitations to meet the requirements using modern design techniques; to apply modern design techniques for this purpose.

4

To choose and use the required modern techniques and tools for analysis and solution of complex problems in Biomedical Engineering applications; to skillfully use information technologies.

5

To design and do simulation and/or experiment, collect and analyze data and interpret results for studying complex engineering problems or research topics of the discipline. 

6

To efficiently participate in intradisciplinary and multidisciplinary teams; to work independently.

7

To communicate both in oral and written form in Turkish; to have knowledge of at least one foreign language; to have the skill to write and understand reports, prepare design and production reports, present, give and receive clear instructions.

8

To recognize the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.

9

To behave ethically, to be aware of professional and ethical responsibilities; to have knowledge about the standards in Biomedical Engineering applications.

10

To have information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development.

11

To have knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of Biomedical Engineering solutions.

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