FACULTY OF ENGINEERING

Department of Food 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/Spring
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
Elective
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 Being able to transfer knowledge and skills acquired in mathematics and science into engineering,
2 Being able to identify and solve problem areas related to Food Engineering,
3 Being able to design projects and production systems related to Food Engineering, gather data, analyze them and utilize their outcomes in practice,
4

Having the necessary skills to develop and use novel technologies and equipment in the field of food engineering,

5

Being able to take part actively in team work, express his/her ideas freely, make efficient decisions as well as working individually,

6

Being able to follow universal developments and innovations, improve himself/herself continuously and have an awareness to enhance the quality,

7

Having professional and ethical awareness,

8 Being aware of universal issues such as environment, health, occupational safety in solving problems related to Food Engineering,
9

Being able to apply entrepreneurship, innovativeness and sustainability in the profession,

10

Being able to use software programs in Food Engineering and have the necessary knowledge and skills to use information and communication technologies that may be encountered in practice (European Computer Driving License, Advanced Level),

11

Being able to gather information about food engineering and communicate with colleagues using a foreign language ("European Language Portfolio Global Scale", Level B1)

12

Being able to speak a second foreign language at intermediate level.

13

Being able to relate the knowledge accumulated during the history of humanity to the field of expertise

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

 


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