To teach basic concepts of linear algebra for engineering students
Prerequisite(s)
None
Corequisite(s)
None
Special Requisite(s)
None
Instructor(s)
Assoc. Prof. Ayten KOÇ
Course Assistant(s)
__
Schedule
Doc.Dr. Ayten Koc: Section A Monday 09:00-11:00 (B1-5), Wednesday 13:00-15:00 (3C0406); Section B Monday 11:00-13:00 (2B0305), Wednesday 15:00-17:00 (B1-7).
Office Hour(s)
Doc.Dr. Ayten Koc, Tuesday 11:00-12:00 (3A-01).
Teaching Methods and Techniques
Lecture, discussion
Principle Sources
B.Kolman-Dr.Hill, Elementary Linear Algebra with Aplications, Pearson International Edition, 9/E(2013), ISBN 0-13-135063-3.
Other Sources
H.Anton-C.Rorres, Elementary Linear Algebra , Jhon Wiley&sons,Inc.(2011),ISBN 978-0-470-56157-7.
-B.Kolman-Dr.Hill, Introductory Linear Algebra, Prentice-Hall (2005), ISBN 0-13-127773-1.
-Fraleigh-Beauregard, Linear Algebra, Addison8-Wesley (1995).
- E.M.Landesman-M.R.Hestenes, Linear Algebra for Mathematics, Science, and Engineering,Prentice- Hall,Inc(1992)
-S. Lipschutz, M. Lipson, Schaum’s Outline of Linear Algebra, Mc Graw-Hill Companies,The Pub.Date: December 2000,ISBN-13:9780071362009.
-Any textbook on advanced linear algebra.
Course Schedules
Week
Contents
Learning Methods
1. Week
Matrices; Matrix Operations,
Oral and written presentation
2. Week
Algebraic Properties of Matrix Operations, Special Types of Matrices
Oral and written presentation
3. Week
Row Echelon Form of a Matrix
Oral and written presentation
4. Week
Solving Linear Systems; Homogeneous Systems
Oral and written presentation
5. Week
Elementary Matrices and Finding the Inverse of a Matrix by Using Elementary Operations
Oral and written presentation
6. Week
Determinants; Definition and Properties of Determinants
Oral and written presentation
7. Week
Cofactor Expansion; Finding Inverses by Using Cofactors
Oral and written presentation
8. Week
Cramer’s Rule; Rank of a Matrix
Oral and written presentation
9. Week
Vector Spaces: Definition; Subspaces
Oral and written presentation
10. Week
Span and Linear Independence
Oral and written presentation
11. Week
Basis and Dimensions, Coordinates,
Inner Product Spaces
Oral and written presentation
12. Week
Eigenvalues and Eigenvectors
Oral and written presentation
13. Week
Diagonalization and Similar Matrices
Oral and written presentation
14. Week
Linear Transformation
Oral and written presentation
15. Week
Final Examinations
written
16. Week
Final Examinations
written
17. Week
Final Examinations
written
Assessments
Evaluation tools
Quantity
Weight(%)
Program Outcomes
PO-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.
PO-2
Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modelling methods for this purpose.
PO-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.)
PO-4
Ability to devise, select, and use modern techniques and tools needed for engineering practice; ability to employ information technologies effectively.
PO-5
Ability to design and conduct experiments, gather data, analyse and interpret results for investigating engineering problems.
PO-6
Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
PO-7
Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language.
PO-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.
PO-9
Awareness of professional and ethical responsibility.
PO-10
Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development.
PO-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 Outcomes
LO-1
Recognize special type of matrices and perform the Matrix operations.
LO-2
Solve linear systems by Gauss-Jordan reduction.
LO-3
Find the transpose, inverse, rank and adjoint of a matrix.
LO-4
Calculate determinants using row operations, column operations, and cofactor expansion along any row ( or column).
LO-5
Solve linear systems by Cramer’s rule.
LO-6
Prove algebraic statements about vector addition, scalar multiplication, linear independence, spanning sets, subspaces, bases, and dimension.
LO-7
Calculate eigenvalues and their corresponding eigenvectors of a square matrix.
LO-8
Prove the properties of eigenvalues and eigenvectors.
LO-9
Determine if a matrix is diagonalizable, and if it is, diagonalize it.
