Industrial Engineering
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Ders Genel Tanıtım Bilgileri

Course Code:

FEC209

Ders İsmi:

Mühendislik Matematiği

Ders Yarıyılı:

Fall

Ders Kredileri:

Theoretical	Practical	Laboratory	ECTS
3	0	0	3

Language of instruction:

Turkish

Ders Koşulu:

Ders İş Deneyimini Gerektiriyor mu?:

Type of course:

Required

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 :

Asst. Prof. Dr. MELİSA RAHEBİ

Course Lecturer(s):

Course Assistants:

Dersin Amaç ve İçeriği

Course Objectives:	The aim of this course is to teach advanced mathematical concepts required in the fields of engineering and natural sciences, and to develop students’ problem-solving and analytical thinking skills in topics such as vectors and curves in three-dimensional space, coordinate systems, integral theorems, and complex analysis
Course Content:	Vectors and Geometry; Curve Analysis; Orthogonal Coordinate Systems and Transformations Between Coordinate Systems; Differential Elements; Metric Coefficients and the Del (Nabla) Operator; Vector Differential Calculus; Helmholtz Theorem; Double and Triple Integrals; Vector Integral Calculus; Integral Theorems; Arithmetic Operations, Differentiation, and Integration in Complex Numbers

Learning Outcomes

The students who have succeeded in this course;

Learning Outcomes

1 - Knowledge
Theoretical - Conceptual
1) Learns vector, line, plane, and curve analysis in R³ (arc length, unit tangent vector, curvature, and unit normal vector) and gains applied problem-solving skills.
2) Understands orthogonal coordinate systems (Cartesian, cylindrical, spherical), differential elements, and the Del (Nabla) operator, and applies them in engineering problems.
3) Learns multiple integrals (double and triple integrals), as well as line and surface integrals, and applies them in engineering applications.
2 - Skills
Cognitive - Practical
1) Learns integral theorems (Green’s, Gauss’s, and Divergence theorems) and integral calculus in complex numbers; understands the Helmholtz Theorem and is able to compute the divergence and curl of given functions.
3 - Competences
Communication and Social Competence
Learning Competence
Field Specific Competence
Competence to Work Independently and Take Responsibility

Ders Akış Planı

Week	Subject	Related Preparation
1)	Vectors, Lines, and Planes in R³ and Their Properties
2)	Curve Analysis: Arc Length, Unit Tangent Vector, Curvature, and Unit Normal Vector
3)	Orthogonal Coordinate Systems: Cartesian, Cylindrical, and Spherical
4)	Transformations Between Coordinate Systems
5)	Differential Elements: Length, Surface, and Volume in Orthogonal Coordinate Systems
6)	Metric Coefficients and the Nabla Operator: Gradient of Scalar Functions
7)	Vector Differential Calculus: Divergence and Curl
8)	midterm exam
9)	Helmholtz Theorem: Calculation of Divergence and Curl of Vector Function
10)	double integrals
11)	Triple Integrals
12)	Vector Integral Calculus (Line Integral and Surface Integral)
13)	Integral Theorems: Green’s, Gauss’s, and Divergence Theorems
14)	Complex Numbers: Arithmetic Operations, Differentiation, and Integration
15)	Final

Sources

Course Notes / Textbooks:
References:	1. Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition, Wiley, 2015. 2. F. B. Hildebrand, Advanced Calculus for Applications, 2nd Edition, Prentice-Hall, 1976

Ders - Program Öğrenme Kazanım İlişkisi

Ders Öğrenme Kazanımları	1	2	3	4
Program Outcomes
1) Adequate knowledge in the fields of mathematics and science; ability to use theoretical and practical knowledge in these fields.
2) Adequate knowledge in subjects specific to the relevant engineering discipline; ability to use theoretical and applied knowledge in these areas to solve complex engineering problems.
3) Ability to identify, formulate and solve complex engineering problems.
4) Ability to select and apply appropriate analysis and modeling methods to complex engineering problems.
5) The ability to design a complex system, process, device or product under realistic constraints and conditions to meet specific requirements.
6) Ability to apply modern design methods to design a complex system, process, device or product.
7) Ability to select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering practice.
8) Ability to use information technologies effectively to analyze and solve complex problems encountered in engineering applications.
9) Ability to design and conduct experiments to investigate complex engineering problems or discipline-specific research topics.
10) Ability to collect data, analyze and interpret results for the investigation of complex engineering problems or discipline-specific research topics.
11) Ability to work effectively in disciplinary teams.
12) Ability to work effectively in multidisciplinary teams.
13) Individual working skills.
14) Ability to communicate effectively both orally and in writing.
15) Knowledge of at least one foreign language.
16) Effective report writing and comprehension of written reports, ability to prepare design and production reports.
17) Ability to make effective presentations, give and receive clear and understandable instructions.
18) Awareness of the necessity of lifelong learning.
19) Ability to access information, to follow developments in science and technology and to continuously renew oneself.
20) Knowledge about acting in accordance with ethical principles, professional and ethical responsibility and standards used in engineering practices.
21) Knowledge of business practices such as project management, risk management and change management.
22) Awareness about entrepreneurship and innovation.
23) Knowledge about sustainable development.
24) Knowledge about the effects of engineering applications on health, environment and safety in universal and social dimensions and the problems of the era reflected in the field of engineering.
25) Awareness of the legal implications of engineering solutions.

Ders - Öğrenme Kazanımı İlişkisi

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Program Outcomes	Level of Contribution
1)	Adequate knowledge in the fields of mathematics and science; ability to use theoretical and practical knowledge in these fields.	5
2)	Adequate knowledge in subjects specific to the relevant engineering discipline; ability to use theoretical and applied knowledge in these areas to solve complex engineering problems.	4
3)	Ability to identify, formulate and solve complex engineering problems.	5
4)	Ability to select and apply appropriate analysis and modeling methods to complex engineering problems.	4
5)	The ability to design a complex system, process, device or product under realistic constraints and conditions to meet specific requirements.
6)	Ability to apply modern design methods to design a complex system, process, device or product.
7)	Ability to select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering practice.
8)	Ability to use information technologies effectively to analyze and solve complex problems encountered in engineering applications.
9)	Ability to design and conduct experiments to investigate complex engineering problems or discipline-specific research topics.
10)	Ability to collect data, analyze and interpret results for the investigation of complex engineering problems or discipline-specific research topics.
11)	Ability to work effectively in disciplinary teams.
12)	Ability to work effectively in multidisciplinary teams.
13)	Individual working skills.
14)	Ability to communicate effectively both orally and in writing.
15)	Knowledge of at least one foreign language.
16)	Effective report writing and comprehension of written reports, ability to prepare design and production reports.
17)	Ability to make effective presentations, give and receive clear and understandable instructions.
18)	Awareness of the necessity of lifelong learning.
19)	Ability to access information, to follow developments in science and technology and to continuously renew oneself.
20)	Knowledge about acting in accordance with ethical principles, professional and ethical responsibility and standards used in engineering practices.
21)	Knowledge of business practices such as project management, risk management and change management.
22)	Awareness about entrepreneurship and innovation.
23)	Knowledge about sustainable development.
24)	Knowledge about the effects of engineering applications on health, environment and safety in universal and social dimensions and the problems of the era reflected in the field of engineering.
25)	Awareness of the legal implications of engineering solutions.

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Midterms	1	% 50
Final	1	% 50
total		% 100
PERCENTAGE OF SEMESTER WORK		% 50
PERCENTAGE OF FINAL WORK		% 50
total		% 100