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| INS2030 | Engineering Mathematics | 4+0+0 | ECTS:5 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of CIVIL ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Erhan COŞKUN | | Co-Lecturer | DOCTOR LECTURER Ayşe KABATAŞ,DOCTOR LECTURER Tuncay KÖROĞLU, | | 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.
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| 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 equation | 1 | 1 | | LO - 2 : | gain the knowledge and experience in solving constant coefficient heat, wave and potantial equation | 1 | 1 | | LO - 3 : | gain the knowledge and experience in complex numbers and basic theory of complex functions with some applications. | 1 | 1 | | LO - 4 : | calculate contour integrals,Taylor and Laurent expansions and use the calculus of residues to evaluate integrals | 1 | 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 | | |
| Fourier series. Fourier sinus and cosinus series. Solutions of heat and wave equation using separation of variables. 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. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Introducation
| | | Week 2 | Fourier series | | | Week 3 | Fourier sine and cosine serier | | | Week 4 | Heat equation and solution with separation of variables | | | Week 5 | Wave equation and solution | | | Week 6 | Introduction to complex numbers and their properties | | | Week 7 | Complex functions | | | Week 8 | Graph of complex functions | | | Week 9 | Mid-term exam | | | Week 10 | Limit and continuity in complex functions | | | Week 11 | Derivative analytic and harmonic functions | | | Week 12 | Line integrals of the complex functions | | | Week 13 | Cauchy derivative and integration formulas | | | Week 14 | Taylor and Laurent series | | | Week 15 | Rezidue and its applications | | | Week 16 | Final examination | | | |
| 1 | KREYSZIG, E. 1997; Advenced Engineering Mathematics, New York. | | | |
| 1 | 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 | 08/04/2017 | 2 | 50 | | End-of-term exam | 16 | 05/06/2017 | 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 | 4 | 14 | 56 | | Laboratuar çalışması | 0 | 0 | 0 | | Arasınav için hazırlık | 4 | 4 | 16 | | Arasınav | 1 | 1 | 1 | | Uygulama | 0 | 0 | 0 | | Klinik Uygulama | 0 | 0 | 0 | | Ödev | 0 | 0 | 0 | | Proje | 0 | 0 | 0 | | Kısa sınav | 0 | 0 | 0 | | Dönem sonu sınavı için hazırlık | 4 | 4 | 16 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 0 | 0 | 0 | | Diğer 2 | 0 | 0 | 0 | | Total work load | | | 147 |
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