Department of Electrical and Electronics Engineering

EEE 281 | Course Introduction and Application Information

Course Name

Engineering Mathematics I

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
EEE 281	FALL	2	2	3	6

Prerequisites	To be successful in MATH 153 (To have received at least DD grade)
Course Language	English
Course Type	Required (Core Course)
Course Level	First Cycle
Mode of Delivery	Face-To-Face
Teaching Methods and Techniques of the Course	Lecture / Presentation Problem Solving
National Occupational Classification Code	-
Course Coordinator	Prof. Dr. Murat Aşkar
Course Lecturer(s)	Prof. Dr. Murat Aşkar
Assistant(s)	-

Course Objectives

Introduction to Complex Algebra. Representation of Complex Numbers. Euler Formula. Complex Functions. Analytical Functions. Matrices. System of Linear Equations. Gauss-Elimination Method. Linear Dependency and Independence. Vector Spaces. Determinants. Inverse Matrix. Eigenvalue Problem and Diagonalization. First and Second Order Differential Equations. Linear Constant Coefficient Differential Equations. Euler Method. Separable and Ordinary Differential Equations. Modeling Engineering Problems with Differential Equations. System of Linear Differential Equations.

Learning Outcomes

The students who succeeded in this course;

Name	Description	PC Sub	* Contribution Level
Name	Description	PC Sub	1	2	3	4	5
LO1	Performs operations related to complex algebra and complex functions,	1.1			X
LO2	Solve linear algebraic equations using matrix properties,	1.1			X
LO3	Solve eigenvalue and eigenvector problems and vector space problems related to matrices,	1.1		X
LO4	Solve first and second order differential equations by modelling differential equations,	1.1			X
LO5	Solve systems of linear first order differential equations by modelling them,	1.1			X
LO6	Using complex numbers, matrices, differential equations in solving engineering problems,	4	X

Course Description

Complex Numbers and Their Geometric Representations. Analytical Functions and Properties. Cauchy-Riemann Equations. Laplace Equation. Euler Formula. Line Integral in the Complex Plane. Cauchy Integral Theorem. Matrices and Vectors. Matrix Operations. Systems of Linear Equations. Gauss Elimination. Linear Independence. Matrix Order. Vector Space. Linear System Solutions. Cramer's Rule. Determinants. Eigenvalues and Eigenvalue Vectors. Orthogonal Matrices. Eigenvalue Basis Vectors. Diagonalization. Gram-Schmidt Orthogonalization Method. Basic Concepts in Differential Equations. Modeling. Euler Method. Separable and Ordinary Differential Equations (OTD). First and Second Order Homogeneous Linear Differential Equations. Linear Differential Equations with Constant Coefficients. Modeling Engineering Problems with Differential Equations. System of Linear Differential Equations. Modeling and Solution of Systems of Linear Differential Equations.

Related Sustainable Development Goals

Course Category	Core Courses	X
	Major Area Courses
	Supportive Courses
	Media and Managment Skills Courses
	Transferable Skill Courses

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week	Subjects	Required Materials	Learning Outcome
1	Complex numbers and Geometric Representation. Polar Form. Receiving strength and finding root. Derivative. Analytical Function.	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 13.1, 13.2, 13.3)	99a7db87
2	Cauchy-Riemann Equation. Laplace Equation. Exponential , Logarithmic, Trigonometric and Hyperbolic Functions. Euler's Formula	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 13.4, 13.5, 13.6, 13.7)	99a7db87
3	Line Integral in the Complex Plane, Cauchy Integral Theorem, Derivative of Analytic Functions	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 14.1, 4.2, 14.3, 14.4)	99a7db87
4	Matrices, Vectors. Addition, Multiplication by constant number, Matrix Multiplication. Linear Equation System. Gauss Elimination Method	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 7.1, 7.2, 7.3)	3afdd132
5	Linearly Independent Vectors. Order of Matrices. Vector Spaces. Solution of Linear Systems. Issues of Existence and Uniqueness. Second and Third Degree Determinants. Inverse Matrix. Cramer's Rule. Gauss-Jordan Elimination Method	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 7.4, 7.5, 7.6, 7.7, 7.8)	3afdd132
6	Vector Spaces, Inner Product Spaces, Linear Transformation. Matrix Eigenvalue Problems. Finding Eigenvalue and Eigenvectors. Perpendicular Vectors.	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 7.9, 8.1)	d36ea250
7	Midterm Exam	-	-
8	Applications of Eiegenvalue Problems. Symmetric and Skewed Symmetric and Orthogonal Vectors	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 8.2, 8.3)	d36ea250
9	Eigenbase Vectors. Diagonalization. Second Degree Forms. Gram-Schmidt Perpendicular Generation Method	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 8.4)	d36ea250
10	Differential Equations. Basic Concepts. Modeling. Euler Method. Separable Ordinary Differential Equations (STD).	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 1.1, 1.2, 1.3)	84d33c7b
11	Complete Ordinary Differential Equations. Linear Ordinary Differential Equations.	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 1.4, 1.5, 1.7)	84d33c7b
12	Homogeneous Quadratic and Linear Ordinal Differential Equations. Non-homogeneous Ordinal Differential Equations. Applications.	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 2.1, 2.2, 2.4)	84d33c7b
13	Homogeneous Linear Ordinary Differential Equations, Constant Coefficient Linear Differential Equations and Systems	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 2.6, 2.7, 2.8, 2.9)	ad7fac02
14	Systems of Ordinary Differential Equations, Systems of Ordinary Differential Equations in Engineering Applications. Fixed Coefficient Sytems.	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 3.1, 3.2, 3.3)	ad7fac02
15	Using Complex Numbers, Matrices, Differential Equations in Solving Engineering Problems.	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 4.1, 4.2, 4.3)	8b254dc6
16	Final Exam	-	-

Course Notes/Textbooks	Erwin Kreyszig "Advanced Engineering Mathematics" 10th Ed Wiley 2011. ISBN: 978-0-470-45836-5.
Suggested Readings/Materials	"Diiferential Equations and Linear Algebra" 3/E Edwards & Penney 2010 Prentice Hall ISBN: 978-0-138-14102-8

EVALUATION SYSTEM

Semester Activities	Number	Weighting	LO1	LO2	LO3	LO4	LO5	LO6
Quizzes / Studio Critiques	3	20	X	X	X	X	X
Homework / Assignments	1	5	X		X	X	X	X
Midterm	1	35	X	X	X
Final Exam	1	40	X	X	X	X	X	X
Total	6	100

ECTS / WORKLOAD TABLE

Semester Activities	Number	Duration (Hours)	Workload
Participation	-	-	-
Theoretical Course Hours	16	4	64
Laboratory / Application Hours	-	-	-
Study Hours Out of Class	16	3	48
Field Work	-	-	-
Quizzes / Studio Critiques	3	5	15
Portfolio	-	-	-
Homework / Assignments	5	4	20
Presentation / Jury	-	-	-
Project	-	-	-
Seminar / Workshop	-	-	-
Oral Exams	-	-	-
Midterms	1	9	9
Final Exam	1	24	24
		Total	180

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	Engineering Knowledge: Knowledge of mathematics, science, basic engineering, computation, and related engineering discipline-specific topics; the ability to apply this knowledge to solve complex engineering problems.
	1	Mathematics		LO3	LO1 LO2 LO4 LO5
	2	Science
	3	Basic Engineering
	4	Computation
	5	Related engineering discipline-specific topics
	6	The ability to apply this knowledge to solve complex engineering problems
2	Problem Analysis: Ability to identify, formulate and analyze complex engineering problems using basic knowledge of science, mathematics and engineering, and considering the UN Sustainable Development Goals relevant to the problem being addressed.
3	Engineering Design: The ability to devise creative solutions to complex engineering problems; the ability to design complex systems, processes, devices or products to meet current and future needs, considering realistic constraints and conditions.
	1	Ability to design creative solutions to complex engineering problems
	2	Ability to design complex systems, processes, devices or products to meet current and future needs, considering realistic constraints and conditions
4	Use of Techniques and Tools: Ability to select and use appropriate techniques, resources, and modern engineering and computing tools, including estimation and modeling, for the analysis and solution of complex engineering problems, while recognizing their limitations.		LO6
5	Research and Investigation: Ability to use research methods to investigate complex engineering problems, including literature research, designing and conducting experiments, collecting data, and analyzing and interpreting results.
	1	Literature research for the study of complex engineering problems
	2	Designing experiments
	3	Ability to use research methods, including conducting experiments, collecting data. analyzing and interpreting results
6	Global Impact of Engineering Practices: Knowledge of the impacts of engineering practices on society, health and safety, economy, sustainability, and the environment, within the context of the UN Sustainable Development Goals; awareness of the legal implications of engineering solutions.
	1	Knowledge of the impacts of engineering practices on society, health and safety, economy, sustainability, and the environment, within the context of the UN Sustainable Development Goals
	2	Awareness of the legal implications of engineering solutions
7	Ethical Behavior: Acting in accordance with the principles of the engineering profession, knowledge about ethical responsibility; awareness of being impartial, without discrimination, and being inclusive of diversity.
	1	Acting in accordance with the principles of the engineering profession, knowledge about ethical responsibility ethical responsibility
	2	Awareness of being impartial and inclusive of diversity, without discriminating on any subject
8	Individual and Teamwork: Ability to work effectively, individually and as a team member or leader on interdisciplinary and multidisciplinary teams (face-to-face, remote or hybrid).
	1	Ability to work individually and within the discipline
	2	Ability to work effectively as a team member or leader in multidisciplinary teams (face-to-face, remote or hybrid)
9	Verbal and Written Communication: Taking into account the various differences of the target audience (such as education, language, profession) on technical issues.
	1	Ability to communicate verbally
	2	Ability to communicate effectively in writing
10	Project Management: Knowledge of business practices such as project management and economic feasibility analysis; awareness of entrepreneurship and innovation.
	1	Knowledge of business practices such as project management and economic feasibility analysis
	2	Awareness of entrepreneurship and innovation
11	Lifelong Learning: Lifelong learning skills that include being able to learn independently and continuously, adapting to new and developing technologies, and thinking questioningly about technological changes.