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| DUM2014 | Engineering Mathematics | 4+0+0 | ECTS:6 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of MARITIME TRANSPORTATION and MANAGEMENT ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Doç. Dr. Devran YAZIR | | Co-Lecturer | Assoc. Prof. Dr. Devran YAZIR | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim 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. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | Gain the knowledge and experience in solving second-order common ordinary differential differential equations with variable coefficients. | 1,4 | 1, | | LO - 2 : | Gain the knowledge and experience in solving constant coefficient heat, wave and potantial equation. | 1,4 | 1, | | LO - 3 : | Gain the knowledge and experience in complex numbers and basic theory of complex functions with some applications.
| 1,4 | 1, | | LO - 4 : | Calculate contour integrals, Taylor and Laurent expansions, and use the calculus of residues to evaluate integrals. | 1,4 | 1, | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome | | |
| Introduction to power series, Series solutions near ordinary points, Uniform singular points, Frobenious method, Bessel equation and applications, Periodic functions, Fourier series and applications, Heat equation and separation of variables, One-dimensional wave equation, Steady temperature distribution and Laplace equations, Sturm-Liouville problems and eigenfunction expansions, Complex numbers and functions, Limit, Continuity, Derivative and integral of Complex functions . Cauch integral and derivative theorems and their applications. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Fourier series and convergence of general Fourier series. | | | Week 2 | Fourier sinus and cosinus series, solution of differential equations with Fourier series. | | | Week 3 | Introduction to first and second order partial differential equations.
| | | Week 4 | Solutions of heat and wave equation using separation of variables and Laplace transformation. | | | Week 5 | Sturm-Liouville problems and eigenfunction expansions. | | | Week 6 | Introduction to complex numbers and properties. | | | Week 7 | Concept of complex functions. | | | Week 8 | Conformal mapping. | | | Week 9 | Mid-term exam | | | Week 10 | Limit, continuity, and derivative in complex functions. | | | Week 11 | Concept of analytical and harmonic functions. | | | Week 12 | Integration of complex functions. | | | Week 13 | Cauchy integration theorems and applications. | | | Week 14 | Cauchy derivative theorems and applications. | | | Week 15 | Taylor and Laurent series. Residue Theorem and application to the calculation of real integrals. | | | Week 16 | End-of-term exam | | | |
| 1 | Edwards, C.H., Penney, D.E. (Çeviri Ed. AKIN, Ö). 2006; Diferensiyel Denklemler ve Sınır Değer Problemleri (Bölüm 1-7), Palme Yayıncılık, Ankara. | | | 2 | Edwards, C.H., Penney, D.E. (Çeviri Ed. AKIN, Ö). 2006; Diferensiyel Denklemler ve Sınır Değer Problemleri (Bölüm 1-7), Palme Yayıncılık, Ankara. | | | |
| 1 | KREYSZIG, E. 1997; Advenced Engineering Mathematics, New York. | | | 2 | Başkan, T. 2005.;Kompleks Fonksiyonlar Teorisi, Nobel Yayınları, Ankara. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 16/04/2024 | 2 | 50 | | End-of-term exam | 16 | 10/06/2024 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 4 | 15 | 60 | | Sınıf dışı çalışma | 2 | 15 | 30 | | Arasınav için hazırlık | 9 | 2 | 18 | | Ödev | 2 | 9 | 18 | | Dönem sonu sınavı | 15 | 2 | 30 | | Total work load | | | 156 |
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