ENERGY SYSTEMS OPERATION AND TECHNOLOGIES (ENGLISH, NONTHESIS)
Master TR-NQF-HE: Level 7 QF-EHEA: Second Cycle EQF-LLL: Level 7

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT5101 Engineering Mathematics Fall 3 0 3 8
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: Turkish
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Prof. Dr. MESUT EROL SEZER
Course Lecturer(s): Assist. Prof. CAVİT FATİH KÜÇÜKTEZCAN
Recommended Optional Program Components: None
Course Objectives: To equip the student with advanced topics of vector calculus and complex calculus.

Learning Outcomes

The students who have succeeded in this course;
The student will be able to understand differences and similarities of fundamental mathematical concepts as they apply to functions of a single variable or several variables, and to apply concepts of advanced calculus and complex calculus to engineering problems

Course Content

Vector differential and integral calculus, and applications. Complex calculus and applications. Fourier series and Fourier transform.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Review of single-variable calculus.
2) Functions of several variables. Partial derivatives, differentials, implicit functions, Jacobian.
3) Vector functions. Gradient, divergence, curl and Laplacian. Directional derivative.
4) Maxima and minima, Lagrange multipliers.
5) Multiple integrals. Line integrals, Green's theorem.
6) Surface integrals, the divergence theorem, Stoke's theorem.
7) Cylindrical and spherical coordinates.
8) Applications of vector calculus.
9) Functions of a complex variable. Continuity and differentiation.
10) Complex integration. Cauchy's theorem and integral formula.
11) Taylor and Laurent series. Poles and residues.
12) Conformal mapping and applications.
13) Fourier series.
14) Fourier transform.

Sources

Course Notes / Textbooks:
References: 1. D. Bachman, Advanced Calculus Demystified, McGraw-Hill, 2007.
2. F. J. Flanigan, Complex Variables, Dover, 1983.

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Attendance 15 % 15
Homework Assignments 5 % 15
Midterms 1 % 30
Final 1 % 40
Total % 100
PERCENTAGE OF SEMESTER WORK % 60
PERCENTAGE OF FINAL WORK % 40
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Study Hours Out of Class 14 7 98
Homework Assignments 5 5 25
Midterms 1 10 10
Final 1 15 15
Total Workload 190

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) To be able to follow scientific literature, analyze it critically and use it effectively in solving engineering problems.
2) Develops his/her knowledge in the field of Energy Systems Engineering to the level of specialization. 3
3) To be able to carry out studies related to Energy Systems Engineering independently, take scientific responsibility and evaluate the results obtained from a critical point of view.
4) To be able to present the results of his/her research and projects effectively in written, oral and visual form in accordance with academic standards.
5) To be able to conduct independent research on subjects requiring expertise in Energy Systems Operation and Technology, to develop original thought and to transfer this knowledge to practice.
6) To be able to comprehend the interdisciplinary interactions related to the field of Energy Systems Engineering. 5
7) Acts in accordance with professional, scientific and ethical values; takes responsibility by considering the social, environmental and ethical impacts of engineering practices.