| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | İ206B2 | Engineering Mathematics | Compulsory | 2 | 4 | 4 |
|
| Level of Course Unit |
| First Cycle |
| Objectives of the Course |
| This course aims to provide mathematical tools for analysing models in the form of second-order variable-coefficient differential equations and constant coeffficient partial differential equations. Furthermore, an introduction to complex numbers and theory of complex functions are provided. |
| Name of Lecturer(s) |
| Dr. Öğr. Üyesi Ebubekir AKKOYUNLU |
| Learning Outcomes |
| 1 | Gain the knowledge and experience in solving second-order common ordinary differential equation | | 2 | Gain the knowledge and experience in solving constant coefficient heat, wave and potantial equation | | 3 | Gain the knowledge and experience in complex numbers and basic theory of complex functions with some applications. | | 4 | Calculate contour integrals,Taylor and Laurent expansions and use the calculus of residues to evaluate integrals | | 5 | Expressing a vector belonging to different bases and finding its coordinates | | 6 | Calculate the norm of a vector in dot product spaces and determine whether two vectors are orthogonal. | | 7 | Ability to orthogonalize linear independent vectors using the Gram - Schmidt method | | 8 | Ability to solve problems using the properties of linear transformations | | 9 | Gain the knowledge and experience in solving second-order common ordinary differential equation |
|
| Mode of Delivery |
| Normal Education |
| Prerequisites and co-requisities |
| None |
| Recommended Optional Programme Components |
| None |
| Course Contents |
| Fourier series and convergence of general Fourier series. Fourier sinus and cosinus series, solution of differential equations with Fourier series. Introduction to first and second order partial differential equations. Solutions of heat and wave equation using separation of variables and Laplace transformation. Sturm-Liouville problems and eigenfunction expansions. Introduction to complex numbers and properties. Concept of complex functions. Conformal mapping. Limit, continuity and derivative in complex functions. Integration of complex functions. Cauchy integration theorems and applications. Cauchy derivative theorems and applications. Taylor and Laurent series. Residue Theorem and application to calculation of real integrals. |
| Weekly Detailed Course Contents |
|
| 1 | Fourier series and convergence of general Fourier series. | | | | 2 | Fourier sinus and cosinus series, solution of differential equations with Fourier series | | | | 3 | Introduction to first and second order partial differential equations | | | | 4 | Solutions of heat and wave equation using separation of variables and Laplace transformation | | | | 5 | Sturm-Liouville problems and eigenfunction expansions | | | | 6 | Introduction to complex numbers and properties | | | | 7 | Concept of complex functions, conformal mapping | | | | 8 | MID-TERM EXAM
| | | | 9 | Limit, continuity and derivative in complex functions | | | | 10 | Limit, continuity and derivative in complex functions
| | | | 11 | Concept of analytical and harmonic functions | | | | 12 | Integration of complex functions | | | | 13 | Cauchy integration theorems and applications | | | | 14 | Taylor and Laurent series, Residue Theorem and application to calculation of real integrals. | | | | 15 | Taylor and Laurent series, Residue Theorem and application to calculation of real integrals. | | | | 16 | | Final exam | |
|
| Recommended or Required Reading |
| Azer Arastunoğlu Kasımzade. "Mühendislikte DİFERENSİYEL DENKLEMLER", 2021 Ankara, Nobel Yayınları
Peter V. O’Neil, Çeviren:Yaşar Pala, İLERİ MÜHENDİSLİK MATEMATİĞİ - Advanced Engineering Mathematics, 2022 Ankara, Nobel Yayınları. |
| Planned Learning Activities and Teaching Methods |
|
| Assessment Methods and Criteria | |
| Midterm Examination | 1 | 100 | | SUM | 100 | |
| Final Examination | 1 | 100 | | SUM | 100 | | Term (or Year) Learning Activities | 40 | | End Of Term (or Year) Learning Activities | 60 | | SUM | 100 |
| | Language of Instruction | | Turkish | | Work Placement(s) | | None |
|
| Workload Calculation |
|
| Midterm Examination | 1 | 2 | 2 |
| Final Examination | 1 | 2 | 2 |
| Attending Lectures | 14 | 3 | 42 |
| Self Study | 14 | 4 | 56 |
| Individual Study for Mid term Examination | 1 | 7 | 7 |
| Individual Study for Final Examination | 1 | 15 | 15 |
|
| Contribution of Learning Outcomes to Programme Outcomes |
| LO1 | 5 | 5 | 3 | 3 | 3 | 3 | 4 | 3 | 3 | 4 | 4 | 5 | 5 | | LO2 | 3 | 3 | 3 | 5 | 3 | 4 | 5 | 3 | 5 | 3 | 4 | 3 | 5 | | LO3 | 5 | 3 | 4 | 4 | 4 | 5 | 5 | 3 | 3 | 4 | 4 | 4 | 4 | | LO4 | 5 | 5 | 3 | 5 | 3 | 3 | 3 | 4 | 4 | 4 | 4 | 5 | 5 | | LO5 | 5 | 4 | 5 | 4 | 4 | 3 | 5 | 3 | 3 | 5 | 3 | 2 | 4 | | LO6 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 5 | 3 | 5 | 5 | | LO7 | 5 | 4 | 5 | 3 | 4 | 4 | 3 | 3 | 3 | 3 | 3 | 5 | 3 | | LO8 | 3 | 5 | 3 | 5 | 3 | 3 | 3 | 5 | 4 | 5 | 5 | 3 | 4 | | LO9 | 5 | 3 | 3 | 3 | 3 | 4 | 5 | 4 | 5 | 4 | 4 | 4 | 5 |
|
| * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
 |
| |