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 6
The course opens with the approval of the Department at the beginning of each semester

Basic information

Language of instruction: Tr
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Prof. Dr. MESUT EROL SEZER
Course Lecturer(s): Dr. Öğr. Üyesi CAVİT FATİH KÜÇÜKTEZCAN
Course Objectives: To equip the student with advanced topics of vector calculus and complex calculus.

Learning Outputs

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.


Course Notes:
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
Laboratory % 0
Application % 0
Field Work % 0
Special Course Internship (Work Placement) % 0
Quizzes % 0
Homework Assignments 5 % 15
Presentation % 0
Project % 0
Seminar % 0
Midterms 1 % 30
Preliminary Jury % 0
Final 1 % 40
Paper Submission % 0
Jury % 0
Bütünleme % 0
Total % 100
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Laboratory 0 0 0
Application 0 0 0
Special Course Internship (Work Placement) 0 0 0
Field Work 0 0 0
Study Hours Out of Class 14 7 98
Presentations / Seminar 0 0 0
Project 0 0 0
Homework Assignments 5 5 25
Quizzes 0 0 0
Preliminary Jury 0
Midterms 1 10 10
Paper Submission 0
Jury 0
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) Have sufficient theoretical background in mathematics, basic sciences and other related engineering areas and to be able to use this background in the field of energy systems engineering.
2) Be able to identify, formulate and solve energy systems engineering-related problems by using state-of-the-art methods, techniques and equipment.
3) Be able to design and do simulation and/or experiment, collect and analyze data and interpret the results.
4) Be able to access information, to do research and use databases and other information sources.
5) Have an aptitude, capability and inclination for life-long learning.
6) Be able to take responsibility for him/herself and for colleagues and employees to solve unpredicted complex problems encountered in practice individually or as a group member.
7) Develop an understanding of professional and ethical responsibility.
8) Develop an ability to apply the fundamentals of engineering mathematics and sciences into the field of energy conversion.
9) Develop an understanding of the obligations for implementing sustainable engineering solutions.
10) Develop an ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability
11) Realize all steps of a thesis or a project work, such as literature survey, method developing and implementation, classification and discussion of the results, etc.