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| HRT2054 | Engineering Mathematics | 4+0+0 | ECTS:5 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of GEOMATICS ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Dr. Öğr. Üyesi Muhammet YAZICI | | Co-Lecturer | | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | Solving Engineering Mathematics problems |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | They will learn the basic information about complex numbers. | 1.1 | 1, | | LO - 2 : | They will understand the solutions of geophysical problems with their mathematical knowledge. | 1.1 | 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 | | |
| Vector fields, Gradient, Divergence and Curl, Green's Theorem, path independence and potential theory. Surface Integrals, Gauss Divergence Theorem, Stokes Theorem, curvilinear coordinates. Fourier series, Fourier sine and cosine series, integration and derivative of Fourier series, complex Fourier series, filtering of signals. Wave equation, heat equation, potential equation and applications. Complex numbers, Complex functions, limit, continuity and differentiability, Complex integration, Cauchy's theorem, Conformal transformations, solution of Dirichlet problem by conformal transformation. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Vector Functions of One Variable; Velocity and Curvature; Vector Fields and Streamlines; Gradient Field; Divergence and Curl | | | Week 2 | Line Integrals; Green's Theorem; An Extension of Green's Theorem; Path Independence and Potential Theory; Surface Integrals | | | Week 3 | Applications of Surface Integrals; Extension of Green's Theorem to Space; Gauss's Divergence Theorem; Stokes's Theorem; Curvilinear Coordinates; | | | Week 4 | Fourier Series of a Function; Applications; Sine and Cosine Series; Applications | | | Week 5 | Integration and Differentiation of Fourier Series; Phase Angle Form; Complex Fourier Series; Filtering of Signals | | | Week 6 | Derivation of the Wave Equation; Wave Motion on a Range; Applications | | | Week 7 | Characteristics and D'Alembert's Solution; Characteristics and D'Alembert's Solution; Applications | | | Week 8 | Heat Equation; Heat Equation on [0,L]; Applications | | | Week 9 | Mid-term Exam | | | Week 10 | Laplace Equation; Dirichlet Problem for Rectangle | | | Week 11 | Dirichlet Problem for Disk; Poisson Integral Formula; Applications | | | Week 12 | Arithmetic and Geometry of Complex Numbers; Complex Functions; Applications | | | Week 13 | Exponential and Trigonometric Functions; Complex Logarithms; Powers; Applications | | | Week 14 | Integration of a Complex Function; Cauchy's Theorem; Corollaries of Cauchy's Theorem; Applications | | | Week 15 | Conformal Transformations; Construction of Conformal Transformation; Solution of Dirichlet Problem with Conformal Transformation | | | Week 16 | Final Exam | | | |
| 1 | 1. P. V. O'Neil: İleri Mühendislik Matematiği (Advanced Engineering Mathematics, 7. Baskıdan Çeviri), Nobel Akademik Yayıncılık, Ankara, 2013 (Çeviren: Prof. Dr. Yaşar Pala) | | | |
| 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 | | 2 | 50 | | End-of-term exam | 16 | | 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 | | Dönem sonu sınavı için hazırlık | 4 | 1 | 4 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 151 |
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