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 |
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Course Language | English | |||||||||||
Course Type | Elective | |||||||||||
Course Level | First Cycle | |||||||||||
Mode of Delivery | - | |||||||||||
Teaching Methods and Techniques of the Course | Problem SolvingQ&ALecturing / 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;
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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. |
Related Sustainable Development Goals | |
| Core Courses | |
Major Area Courses | ||
Supportive Courses | ||
Media and Managment Skills Courses | ||
Transferable Skill Courses |
Week | Subjects | Required Materials |
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, 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). Bölüm 2.3, 2.5 |
7 | Midterm Exam | |
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 | Partial differential equations : an introduction by Walter A.Strauss. Equations of mathematical physics by A.A. Samarskii. Applied Partial Differential Equations: An Introduction by Alan Jeffrey. |
Semester Activities | Number | Weigthing |
Participation | ||
Laboratory / Application | ||
Field Work | ||
Quizzes / Studio Critiques | 4 | 20 |
Portfolio | ||
Homework / Assignments | ||
Presentation / Jury | ||
Project | ||
Seminar / Workshop | ||
Oral Exam | ||
Midterm | 1 | 30 |
Final Exam | 1 | 50 |
Total |
Weighting of Semester Activities on the Final Grade | 5 | 50 |
Weighting of End-of-Semester Activities on the Final Grade | 1 | 50 |
Total |
Semester 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 | 14 | 3 | 42 |
Field Work | |||
Quizzes / Studio Critiques | 4 | 6 | |
Portfolio | |||
Homework / Assignments | |||
Presentation / Jury | |||
Project | |||
Seminar / Workshop | |||
Oral Exam | |||
Midterms | 1 | 30 | |
Final Exams | 1 | 36 | |
Total | 180 |
# | 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