Course Name Code Semester T+U Hours Credit ECTS
Advanced Numerical Analysis MAT 550 0 3 + 0 3 6
Precondition Courses <p>Numerical Analysis</p>
Recommended Optional Courses <p>Computer Programming I,&nbsp;Computer Programming II,&nbsp;Mathematics Programming</p>
Course Language Turkish
Course Level yuksek_lisans
Course Type Optional
Course Coordinator Doç.Dr. MURAT SARDUVAN
Course Lecturers
Course Assistants
Course Category Field Proper Education
Course Objective

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.

Course Content

Direct methods for solving linear systems, Iterative techniques in matrix algebra, Approximation theory, Approximating eigenvalues, Numerical Solutions of nonlinear systems of equations.

# Course Learning Outcomes Teaching Methods Assessment Methods
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,
Week Course Topics Preliminary Preparation
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
Resources
Course Notes <p>Burden, R.L., Faires, J.D., Numerical Analysis, 9th Edition,&nbsp;Cengage Learning, USA, 2010</p>
Course Resources

1) Türker E. S., Sayısal Analiz Yöntemleri, Sakarya, 2000.

2) Tapramaz R., Sayısal Çözümleme, İstanbul, 2002.

Order Program Outcomes Level of Contribution
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
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 40
1. Ödev 20
1. Performans Görevi (Uygulama) 40
2. Performans Görevi (Uygulama) 0
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
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
Total Workload 156
Total Workload / 25 (Hours) 6.24
dersAKTSKredisi 6