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| JFZ2028 | Engineering Mathematics | 4+0+0 | ECTS:5 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of GEOPHYSICAL ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Dr. Öğr. Üyesi Muhammet YAZICI | | Co-Lecturer | none | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | As part of the introduction on complex analysis , the basics of this theory are taught by focusing on complex integrals. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | describe the basics of complex numbers. | 1,2,5 | | | LO - 2 : | geophysical problems can be solved by mathematical knowledge. | 1,2,5 | | | 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 | | |
| Complex numbers and complex variable functions. Complex ranges and series. Elementary functions, complex integration, Cauchy and Cauchy integral theorems. Residues and its applications and Conform conversion. Laplace and Fourier conversions. |
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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 | Mid-term exam | | | Week 9 | Conformal mapping. | | | 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 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 8-10), 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 | 8 | 30.03.2010 | 2 | 30 | | In-term studies (second mid-term exam) | 12 | 27.04.2010 | 1 | 20 | | End-of-term exam | 16 | 25.05.2010 | 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 | 14 | 56 | | Sınıf dışı çalışma | 6 | 14 | 84 | | Arasınav için hazırlık | 3 | 1 | 3 | | Arasınav | 2 | 1 | 2 | | Kısa sınav | 1 | 1 | 1 | | Dönem sonu sınavı için hazırlık | 4 | 1 | 4 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 152 |
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