| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Advanced Numerıcal Analysıs | MAT 550 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | Numerical Analysis |
| Önerilen Seçmeli Dersler | Computer Programming I, Computer Programming II, Mathematics Programming |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | YUKSEK_LISANS |
| Dersin Türü | Seçmeli |
| Dersin Koordinatörü | Doç.Dr. MURAT SARDUVAN |
| Dersi Verenler | |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Alanına Uygun Öğretim |
| Dersin Amacı | To learn advanced numerical methods theoretically and algorithmically, To analyse complex and many unknowns systems, To gain the ability of establishing numerical algorithm in advanced level. |
| Dersin İçeriği | Direct methods for solving linear systems, Iterative techniques in matrix algebra, Approximation theory, Approximating eigenvalues, Numerical Solutions of nonlinear systems of equations. |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | He/she solves systems of linear equations using direct methods. | Lecture, Question-Answer, Discussion, Drilland Practice, Group Study, Brain Storming, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 2 | He/she investigates some iterative techniques in matrix algebra. | Lecture, Question-Answer, Discussion, Drilland Practice, Group Study, Brain Storming, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 3 | He/she learns approximation theory. | Lecture, Question-Answer, Discussion, Drilland Practice, Group Study, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 4 | He/she solves systems of linear equations using numerical methods. | Lecture, Question-Answer, Discussion, Drilland Practice, Group Study, Brain Storming, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Linear systems of equations, Pivoting strategies, Linear algebra and matrix inversion | |
| 2 | The determinant of a matrix, Matrix factorization | |
| 3 | Special types of matrices, Survey of methods and software | |
| 4 | Norms of vectors and matrices, Eigenvalues and eigenvectors | |
| 5 | The Jacobi and Gauss-Siedel iterative techniques, Relaxation techniques for solving linear systems | |
| 6 | Error bounds and iterative refinement, The conjugate gradient method, Survey of methods and software | |
| 7 | Discrete least squares approximation, Orthogonal polynomials and leaste squares approximation | |
| 8 | Chebyshev polynomials and power series, Rational function approximation | |
| 9 | Trigonometric polynomial approximation, Fast Fourier transform, Survey of methods and software | |
| 10 | Linear Algebra and eigenvalues, Orthogonal matrices and similarity transforms, The power method | |
| 11 | Householder's method, The QR algorithm | |
| 12 | Singular Value Decomposition, Survey of methods and software | |
| 13 | Fixed Points for functions of several variables, Newton’s method, Quasi-Newton methods | |
| 14 | Steepest descent techniques, Homotopy and continuation methods, Survey of methods and software |
| Kaynaklar | |
|---|---|
| Ders Notu | Burden, R.L., Faires, J.D., Numerical Analysis, 9th Edition, Cengage Learning, USA, 2010 |
| Ders Kaynakları | 1) Türker E. S., Sayısal Analiz Yöntemleri, Sakarya, 2000. 2) Tapramaz R., Sayısal Çözümleme, İstanbul, 2002. |
| Sıra | Program Çıktıları | Katkı Düzeyi | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 0 | Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise | ||||||
| 2 | Student follows the current journals in his/her field and puts forward problems. | X | |||||
| 3 | Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics | X | |||||
| 4 | Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. | X | |||||
| 5 | Student uses different proof methods to come to a solution by analyzing the problems encountered. | X | |||||
| 6 | Student determines the problems to be solved within his/her field and if necessary takes the lead. | X | |||||
| 7 | Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. | X | |||||
| 8 | Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters | X | |||||
| 9 | Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. | X | |||||
| 10 | Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. | X | |||||
| 11 | Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. | X | |||||
| Değerlendirme Sistemi | |
|---|---|
| Yarıyıl Çalışmaları | Katkı Oranı |
| 1. Ara Sınav | 40 |
| 1. Ödev | 20 |
| 1. Performans Görevi (Uygulama) | 40 |
| 2. Performans Görevi (Uygulama) | 0 |
| Toplam | 100 |
| 1. Yıl İçinin Başarıya | 50 |
| 1. Final | 50 |
| Toplam | 100 |
| AKTS - İş Yükü Etkinlik | Sayı | Süre (Saat) | Toplam İş Yükü (Saat) |
|---|---|---|---|
| Course Duration (Including the exam week: 16x Total course hours) | 16 | 3 | 48 |
| Hours for off-the-classroom study (Pre-study, practice) | 16 | 3 | 48 |
| Mid-terms | 1 | 15 | 15 |
| Assignment | 1 | 10 | 10 |
| Final examination | 1 | 20 | 20 |
| Performance Task (Application) | 1 | 15 | 15 |
| Toplam İş Yükü | 156 | ||
| Toplam İş Yükü / 25 (Saat) | 6,24 | ||
| Dersin AKTS Kredisi | 6 | ||