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

Basic information

Language of instruction: Tr
Type of course: Must Course
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) Gains an academic background and abilities for making scientific research; analysis, interpretation and application of knowledge in subjects of Mechatronics Engineering. 5
2) Acquires an ability to select, apply and develop modern techniques and methods for mechatronics engineering applications. 2
3) Develops new and innovative ideas, procedures and solutions in the design of mechatronics systems, components and processes. 1
4) Gains an ability for experimental design, data accumulation, data analysis, reporting and implementation. 1
5) Acquires abilities for individual and team-work, communication and collaboration with team members and interdisciplinary cooperation. 1
6) Gains an ability to communicate effectively oral and written; and a knowledge of English sufficient to follow technical developments and terminology. 1
7) Acquires recognition of the need for, and an ability to access and report knowledge, to engage in life-long learning. 3
8) Gains an understanding of universal, social and professional ethics. 1
9) Acquires a knowledge of business-oriented project organization and management; awareness of entrepreneurship, innovation and sustainable development
10) Gains awareness for the impact of mechatronics engineering applications on human health, environmental, security and legal issues in a global and social context.