MATH215 Mathematics IIIIstanbul Okan UniversityDegree Programs Civil Engineering (English)General Information For StudentsDiploma SupplementErasmus Policy StatementNational Qualifications
Civil Engineering (English)
Bachelor TR-NQF-HE: Level 6 QF-EHEA: First Cycle EQF-LLL: Level 6

General course introduction information

Course Code: MATH215
Course Name: Mathematics III
Course Semester: Fall
Course Credits:
Theoretical Practical Credit ECTS
2 2 3 6
Language of instruction: EN
Course Requisites: MATH113 - Mathematics I
MATH113 - Mathematics I
Does the Course Require Work Experience?: No
Type of course: Compulsory
Course Level:
Bachelor TR-NQF-HE:6. Master`s Degree QF-EHEA:First Cycle EQF-LLL:6. Master`s Degree
Mode of Delivery: Face to face
Course Coordinator : Dr.Öğr.Üyesi MESERET TUBA GÜLPINAR
Course Lecturer(s): Prof. Dr. HASAN ÖZEKES
Course Assistants:

Course Objective and Content

Course Objectives: The aim of this course to understand basic concepts of linear algebra ( systems of linear equations and their solutions, the operations of the matrix and vector algebra, evaluations of the determinants and inverse matrix, properties of determinants, Cramer’s Rule, vector spaces, subspaces, linear independence, basis, row space, column space, null space, rank, linear transformations, eigenvalues and eigenvectors, diagonalization, inner product spaces, orthogonality, Gram-Schmidt process, least squares, orthogonal diagonalization and singular value decomposition) and solve problems about it.

Course Content: This course will investigate systems of linear equations and their solutions, the operations of the matrix and vector algebra, evaluations of the determinants and inverse matrix, properties of determinants, Cramer’s Rule, vector spaces, subspaces, linear independence, basis, row space, column space, null space, rank, linear transformations, eigenvalues and eigenvectors, diagonalization, inner product spaces, orthogonality, Gram-Schmidt process, least squares, orthogonal diagonalization and singular value decomposition.

Learning Outcomes

The students who have succeeded in this course;
Learning Outcomes
1 - Knowledge
Theoretical - Conceptual
1) Able to calculate the set of all solutions for systems of linear equations if it exists, by using row echelon or reduced row echelon forms. Calculate the inverse of a square matrix, if it exists, using reduced row echelon form or elementary matrices and characterize invertible matrices.
2) Calculate the determinant of a square matrix. Use Cramers Rule to solve linear systems of equations. Determine the linear dependence or independence of a set of nonzero vectors.
3) Identify vectors spaces and subspaces and linear transformations between vector spaces. Calculate basis for null spaces and images of linear transformations. Calculate the representation of linear transformation under various bases.
4) Able to calculate the eigenvalues and the corresponding eigenvectors in order to diagonalize a square matrix by similarity transformation. Characterize diagonalizable matrices
5) Able to use Gram-Schmidt Process to obtain a set of orthogonal vectors and diagonalize a symmetric matrix using orthogonal matrices. Calculate orthogonal projections onto a given subspace and solve the least squares problems. Calculate Singular Value Decomposition of a given matrix.
2 - Skills
Cognitive - Practical
3 - Competences
Communication and Social Competence
Learning Competence
Field Specific Competence
Competence to Work Independently and Take Responsibility

Lesson Plan

Week Subject Related Preparation
1) Syllabus. Systems of linear equations. Elementary row operations. Gauss-Jordan Elimination Lecture Notes
2) Matrix Algebra Lecture Notes
3) Matrix Algebra Lecture Notes
4) Determinants Lecture Notes
5) Determinants Lecture Notes

Sources

Course Notes / Textbooks: Linear Algebra and Its Applications, 5th Edition
David C. Lay, Stephan R. Lay, Judi J. McDonald
Pearson Education Limited

References: Lecture notes - Ders notları

Course-Program Learning Outcome Relationship

Learning Outcomes

1

2

3

4

5

Program Outcomes
1) Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied information in these areas to model and solve engineering problems.
2) Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modelling methods for this purpose.
3) Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way so as to meet the desired result; ability to apply modern design methods for this purpose. (Realistic constraints and conditions may include factors such as economic and environmental issues, sustainability, manufacturability, ethics, health, safety issues, and social and political issues according to the nature of the design.)
4) Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively.
5) Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions.
6) Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
7) Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions.
8) Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
9) Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices.
10) Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development.
11) Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of engineering solutions.

Course - Learning Outcome Relationship

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied information in these areas to model and solve engineering problems. 5
2) Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modelling methods for this purpose.
3) Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way so as to meet the desired result; ability to apply modern design methods for this purpose. (Realistic constraints and conditions may include factors such as economic and environmental issues, sustainability, manufacturability, ethics, health, safety issues, and social and political issues according to the nature of the design.)
4) Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively.
5) Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions.
6) Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
7) Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions.
8) Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
9) Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices.
10) Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development.
11) Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of engineering solutions.

Learning Activity and Teaching Methods

Lesson
Reading
Homework
Problem Solving
Q&A / Discussion

Assessment & Grading Methods and Criteria

Written Exam (Open-ended questions, multiple choice, true-false, matching, fill in the blanks, sequencing)
Homework

Assessment & Grading

Semester Requirements Number of Activities Level of Contribution
Homework Assignments 5 % 20
Midterms 2 % 40
Final 1 % 40
total % 100
PERCENTAGE OF SEMESTER WORK % 60
PERCENTAGE OF FINAL WORK % 40
total % 100

Workload and ECTS Credit Grading

Activities Number of Activities Duration (Hours) Workload
Course Hours 15 4 60
Study Hours Out of Class 15 3 45
Homework Assignments 5 5 25
Midterms 2 10 20
Final 1 15 15
Total Workload 165