ENERGY SYSTEMS OPERATION AND TECHNOLOGY (ENGLISH, THESIS) | |||||

Master | TR-NQF-HE: Level 7 | QF-EHEA: Second Cycle | EQF-LLL: Level 7 |

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 |

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. |

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 |

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

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. |

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 | |

PERCENTAGE OF SEMESTER WORK | % 60 | |

PERCENTAGE OF FINAL WORK | % 40 | |

Total | % 100 |

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 |

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. |