Electrical and Electronic Engineering (English) Preview
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code:

MATH205

Course Name:

Differential Equations

Semester:

Fall

Course Credits:

ECTS

Language of instruction:

English

Course Condition:

Does the Course Require Work Experience?:

Type of course:

Compulsory Courses

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:

Prof. Dr. ŞÜKRÜ YALÇINKAYA

Course Lecturer(s):

Prof. Dr. Ender Abadoğlu

Course Assistants:

Course Objective and Content

Course Objectives:	To make the students know mainly the concepts ordinary differential equations, their solution methods, and their applications in modeling and simulating engineering systems.
Course Content:	Introduction to ordinary differential equations, first order differential equations, second order linear equations, higher order linear equations; series solutions of second order linear equations; the Laplace transform, systems of first order linear equations.

Learning Outcomes

The students who have succeeded in this course;
1) Solve first-order separable and linear differential equations.
2) Find the fundamental solution and the general solution of certain second order linear differential equations.
3) Use the Laplace transform method to solve linear ordinary differential equations.
4) Find the particular solution to a nonhomogeneous linear system of ordinary differential equations.
5) Solve higher-order certain linear differential equations and systems of differential equations.
6) Apply mathematical modelling in areas such as physics, engineering, biology or economics.

Course Flow Plan

Week	Subject	Related Preparation
1)	Introduction, classification of differential equations
2)	First order differential equations: linear equations, method of integrating factors, separable equations, difference between linear and nonlinear equations
3)	Exact equations and integrating factors, existence and uniqueness theorem
4)	Second order linear equations: homogeneous equations with constant coefficients, fundamental solutions of linear homogeneous equations, linear independence, Wronskian.
5)	Complex roots, repeated roots; reduction of order
6)	Nonhomogeneous equations: method of undetermined coefficients, variation of parameters
7)	Higher order linear equations: general theory, homogeneous equations with constant coefficients, method of undetermined coefficients, variation of parameters.
8)	Laplace Transform
9)	The Laplace transform: definitions, solution of initial value problems
10)	Step functions, solution of differential equations with discontinuous forcing functions
11)	Impulse functions, the convolution integral
12)	Systems of first order linear equations: introduction, linear independence, eigenvalues, eigenvectors
13)	Complex eigenvalues, fundamental matrices, repeated eigenvalues, nonhomogeneous linear systems
14)	Series Solutions: power series, series solutions near an ordinary point

Sources

Course Notes / Textbooks:	Boyce, William E.; DiPrima, Richard C., Meade, Douglas B., Elementary Differential Equations and Boundary Value Problems, 12th Edition, Wiley-Blackwell, 2021.
References:	Lecture notes

Course - Program Learning Outcome Relationship

Course Learning Outcomes	1	2	3	4	5	6
Program Outcomes
1) Has sufficient knowledge in mathematics and natural sciences.	3	3	3	3	3	3
2) Has sufficient knowledge in Electrical and Electronics engineering–specific subjects.
3) Has the ability to apply theoretical and practical knowledge of mathematics, natural sciences, and Electrical and Electronics engineering to solve complex engineering problems.
4) Has the ability to identify, formulate, and solve complex engineering problems, and to select and apply appropriate analysis and modeling methods for this purpose.
5) Has the ability to design complex systems, processes, devices, or products under realistic constraints and conditions to meet specific requirements, and to apply modern design methods for this purpose.
6) Has the ability to select and use modern techniques and tools required for the analysis and solution of complex engineering problems encountered in engineering practice, and to use information technologies effectively.
7) Has the ability to design and conduct experiments, collect data, analyze and interpret results for the investigation of complex engineering problems or Electrical and Electronics engineering–specific research topics.
8) Has the ability to work effectively in disciplinary teams.
9) Has the ability to work effectively in multidisciplinary teams.
10) Has the ability to work individually.
11) Has the ability to communicate effectively in oral and written form; has knowledge of at least one foreign language; writes effective reports, understands written reports, prepares design and production reports, makes effective presentations, and gives and receives clear and understandable instructions.
12) Has awareness of the necessity for lifelong learning; accesses information, follows developments in science and technology, and continuously renews oneself.
13) Acts in accordance with ethical principles; has knowledge of professional and ethical responsibilities and of the standards used in engineering practices.
14) Has knowledge of business practices such as project management, risk management, and change management.
15) Has awareness of entrepreneurship and innovation.
16) Has knowledge of sustainable development.
17) Has knowledge of the impacts of engineering practices on health, environment, and safety on a universal and societal scale, and awareness of contemporary issues reflected in the field of engineering.
18) Has awareness of the legal consequences of engineering solutions.

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Average	3 Highest

	Program Outcomes	Level of Contribution
1)	Has sufficient knowledge in mathematics and natural sciences.	3
2)	Has sufficient knowledge in Electrical and Electronics engineering–specific subjects.
3)	Has the ability to apply theoretical and practical knowledge of mathematics, natural sciences, and Electrical and Electronics engineering to solve complex engineering problems.
4)	Has the ability to identify, formulate, and solve complex engineering problems, and to select and apply appropriate analysis and modeling methods for this purpose.
5)	Has the ability to design complex systems, processes, devices, or products under realistic constraints and conditions to meet specific requirements, and to apply modern design methods for this purpose.
6)	Has the ability to select and use modern techniques and tools required for the analysis and solution of complex engineering problems encountered in engineering practice, and to use information technologies effectively.
7)	Has the ability to design and conduct experiments, collect data, analyze and interpret results for the investigation of complex engineering problems or Electrical and Electronics engineering–specific research topics.
8)	Has the ability to work effectively in disciplinary teams.
9)	Has the ability to work effectively in multidisciplinary teams.
10)	Has the ability to work individually.
11)	Has the ability to communicate effectively in oral and written form; has knowledge of at least one foreign language; writes effective reports, understands written reports, prepares design and production reports, makes effective presentations, and gives and receives clear and understandable instructions.
12)	Has awareness of the necessity for lifelong learning; accesses information, follows developments in science and technology, and continuously renews oneself.
13)	Acts in accordance with ethical principles; has knowledge of professional and ethical responsibilities and of the standards used in engineering practices.
14)	Has knowledge of business practices such as project management, risk management, and change management.
15)	Has awareness of entrepreneurship and innovation.
16)	Has knowledge of sustainable development.
17)	Has knowledge of the impacts of engineering practices on health, environment, and safety on a universal and societal scale, and awareness of contemporary issues reflected in the field of engineering.
18)	Has awareness of the legal consequences of engineering solutions.

Assessment & Grading

Değerlendirme Yöntemleri ve Kriterleri	Number of Activities	Level of Contribution
Midterms	1	% 40
Final	1	% 60
total		% 100

Workload and ECTS Credit Calculation

Activities	Number of Activities	Preparation for the Activity	Spent for the Activity Itself	Completing the Activity Requirements	Workload
Course Hours	13	0	3		39
Study Hours Out of Class	13	0	4		52
Midterms	1	18	2		20
Final	1	25	2		27
Total Workload					138