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| HRT2047 | Numerical Analysis | 3+0+0 | ECTS:4 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of GEOMATICS ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Arş. Gör. Fatih TERZİ | | Co-Lecturer | None | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | To give an introduction to numerical calculating processes and numerical solution of a lot of geodetic problems. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | understand number systems and type of errors. | 1 | 1 | | LO - 2 : | know type of enterpolation. | 5 | 1 | | LO - 3 : | make matrix operations. | 1 | 1 | | LO - 4 : | fit curve by LSQ Method. | 15 | 1 | | LO - 5 : | apply numerical differentiation and numerical integration to geodetic problems | 1,15 | 1 | | LO - 6 : | solve equation systems | 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 | | |
| Number systems and errors: The representation of numbers, The number systems, Type of errors in numerical computation and error analysis, Examples. Taylor's series, Binom's series, Examples. The finite difference calculus: Forward and backward differences, Central differences, Examples. Interpolation: Linear interpolation, Non-linear interpolation; Generations of difference table, Lagrange polynomial interpolation, Gregory-Newton interpolation, Central-difference interpolation, Inverse interpolation, Examples. Matrices: The properties of matrices, matrix inversion and the evaluation of determination, Matrix inversion and evaluation of determination by both Gauss-Jordan and Cholesky elimination methods, Examples. Real zeros of function: Finding real zeros of both a linear and non-linear function, real zeros of simultaneous equations: Finding real zeros of both linear and non-linear simultaneous equations. Examples. Curve fitting and functional approximation; Curve fitting by least squares method. Examples. Numerical Differentiation. Numerical Integration, Examples. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Numbers, Number Types and Number Systems, Different Applications. | | | Week 2 | Error and Error Criteria at Numerical Analysis, Error Propogation. | | | Week 3 | Matrix, Inverse of Square Matrix, Triangular Matrix According to Gauss and Cholesky Method. | | | Week 4 | Matrix, Inverse of Square Matrix, Triangular Matrix According to Gauss and Cholesky Method. | | | Week 5 | Find roots which makes zero of single-variable function. | | | Week 6 | Linear Equation Systems, Find roots which makes zero of equation system. | | | Week 7 | Linear Equation Systems, Find roots which makes zero of equation system. | | | Week 8 | Mid-term exam | | | Week 9 | Non-linear Equation Systems and their numerical solutins. | | | Week 10 | Enterpolation Methods, Lagrange Enterpolation. | | | Week 11 | Formula of Gregory-Newton Enterpolation and Applications. | | | Week 12 | Curve Fitting and Sample applications. | | | Week 13 | Curve Fitting and Sample applications. | | | Week 14 | Numerical derivative and Sample Solutions. | | | Week 15 | Numerical integral and Sample Solutions. | | | Week 16 | End-of-term exam | | | |
| 1 | Dilaver, A. 2007; Müdendislikte Sayısal Çözümleme Algoritmaları (Nümerik Analiz). Ders Notu, Trabzon. (Yayımlanmadı) | | | |
| 1 | Karagöz, İ. 2008; Sayısal Analiz ve Mühendislik Uygulamaları, 2. Baskı, Nobel Yayın Dağıtım. | | | 2 | Sönmez, M. 2008; Sayısal Analiz Ders Notları, Aksaray Üniversitesi, İnşaat Mühendisliği Bölümü. | | | 3 | Dikmen, Ü. 2008;Sayısal Analiz ve Programlama III, Ders Notları, | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 8 | 10112010 | 2 | 30 | | Quiz | 13 | 06122010 | 2 | 20 | | End-of-term exam | 16 | 10012011 | 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 | 3 | 14 | 42 | | Sınıf dışı çalışma | 3 | 14 | 42 | | Arasınav için hazırlık | 25 | 1 | 25 | | Arasınav | 2 | 1 | 2 | | Kısa sınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 25 | 1 | 25 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 30 | 1 | 30 | | Total work load | | | 170 |
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