PhD in Mechatronic Engineering (English) with a master's degree | |||||
PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 |
Course Code: | MCHT621 | ||||||||
Course Name: | Advanced Topics in Engineering Mathematics | ||||||||
Course Semester: | Fall | ||||||||
Course Credits: |
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Language of instruction: | EN | ||||||||
Course Requisites: | |||||||||
Does the Course Require Work Experience?: | No | ||||||||
Type of course: | Department Elective | ||||||||
Course Level: |
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Mode of Delivery: | Face to face | ||||||||
Course Coordinator : | Assoc. Prof. ÖMER CİHAN KIVANÇ | ||||||||
Course Lecturer(s): |
Prof. Dr. SEZGİN SEZER |
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Course Assistants: |
Course Objectives: | The objective of this course is to give basic and advanced Mathematic information. |
Course Content: | Calculation of differential and integration of vectors: Vector algebra , gradient, divergent, curl, line integral, Green’s Theorem , The Divergence theorem, Stokes’s theorem. Linear Vector Spaces: Linear Vector Space, Linear operators, vector space of finite dimension, matrix algebra, similarity transforms, eigenvectors and eigenfunctions of matrix, Orthogonal functions: Functions space, orthogonal polynomials, Legendre polynomials, spherical harmonics, Hermite polynomials, Laguerre polynomials, Bessel functions. Complex Functions: Complex numbers, complex functions, derivative of complex functions, concept of analytical function, Conditions of Cauchy-Riemann, Complex integral, Cauchy theorem,Formulas of Cauchy integral, series of complex functions, Laurent series, Residue theorem and its applications. Multiple functions and Riemann surfaces. Differential equations: Series method , power series method, Frobenius’s method, Legendre’s equation, Bessel’s equation, Hermite ‘s equation, Systems of Linear equations. |
The students who have succeeded in this course;
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Week | Subject | Related Preparation |
1) | Calculation of differential and integration of vectors: Vector algebra , gradient, divergent, curl, line integral, Green’s Theorem | Course Notes |
2) | The Divergence theorem, Stokes’s theorem., | Course Notes |
3) | Linear Vector Spaces: Linear Vector Space, Linear operators, vector space of finite dimension, matrix algebra | Course Notes |
4) | Similarity transforms, eigenvectors and eigenfunctions of matrix | Course Notes |
5) | Orthogonal functions: Functions space, orthogonal polynomials, Legendre polynomials | Course Notes |
6) | Spherical harmonics, Hermite polynomials, Laguerre polynomials, Bessel functions | Course Notes |
7) | Complex Functions: Complex numbers, complex functions, derivative of complex functions | Course Notes |
8) | Concept of analytical function, Conditions of Cauchy-Riemann, Complex integral, Cauchy theorem | Course Notes |
9) | Formulas of Cauchy integral, series of complex functions, Laurent series | Course Notes |
10) | Residue theorem and its applications | Course Notes |
11) | Multiple functions and Riemann surfaces | Course Notes |
12) | Differential equations: Series method , power series method | Course Notes |
13) | Frobenius’s method, Legendre’s equation | Course Notes |
14) | Application | Course Notes |
Course Notes / Textbooks: | Higher Engineering Mathematics 44th Edition |
References: | Higher Engineering Mathematics 44th Edition |
Learning Outcomes | 1 |
2 |
3 |
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Program Outcomes | ||||||
1) Knowledge and ability to apply the interdisciplinary synergetic approach of mechatronics to the solution of engineering problems | ||||||
2) Ability to design mechatronic products and systems using the mechatronics approach | ||||||
3) Knowledge and ability to analyze and develop existing products or processes with a mechatronics approach | ||||||
4) Ability to communicate effectively and teamwork with other disciplines | ||||||
5) Understanding of performing engineering in accordance with ethical principles | ||||||
6) Understanding of using technology with awareness of local and global socioeconomic impacts | ||||||
7) Approach to knowing and fulfilling the necessity of lifelong learning |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution | |
1) | Knowledge and ability to apply the interdisciplinary synergetic approach of mechatronics to the solution of engineering problems | |
2) | Ability to design mechatronic products and systems using the mechatronics approach | |
3) | Knowledge and ability to analyze and develop existing products or processes with a mechatronics approach | |
4) | Ability to communicate effectively and teamwork with other disciplines | |
5) | Understanding of performing engineering in accordance with ethical principles | |
6) | Understanding of using technology with awareness of local and global socioeconomic impacts | |
7) | Approach to knowing and fulfilling the necessity of lifelong learning |
Lesson | |
Project preparation |
Written Exam (Open-ended questions, multiple choice, true-false, matching, fill in the blanks, sequencing) | |
Individual Project |
Semester Requirements | Number of Activities | Level of Contribution |
Project | 1 | % 50 |
Final | 1 | % 50 |
total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 50 | |
PERCENTAGE OF FINAL WORK | % 50 | |
total | % 100 |
Activities | Number of Activities | Duration (Hours) | Workload |
Course Hours | 14 | 3 | 42 |
Project | 1 | 175 | 175 |
Final | 1 | 80 | 80 |
Total Workload | 297 |