Applied Numerical Methods I
Mathematics
Institute of Natural and Applied Sciences
Second Cycle (Master's Degree)
| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Applied Numerical Methods I | MAT529 | Elective | Master's degree | 1 | Spring | 8 |
Name of Lecturer(s)
Associate Prof. Dr. Mine Aylin BAYRAK
Associate Prof. Dr. Arzu COŞKUN
Learning Outcomes of the Course Unit
1) Developing mathematical model of the problem by taking advantage of the fundamental concepts of physics and mathematics .
2) Verifying methods for the numerical solution of mathematical models.
3) Making the numerical solution of some problems with the help of MATLAB.
4) Developing algorithms for the numerical solution of mathematical problems using MATLAB codes corresponding to different physical phenomenon
5) Making the physical interpretation of the numerical solutions obtained from the analysis of the results.
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
| Learning Outcomes | ||||||||
| 1 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 2 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 3 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 4 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 5 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Numerical Analysis
Course Contents
This course provides candidates with in-depth knowledge on trigonometric interpolation, spline polinomials of second and third order, least squares method, Mathematical models which are formulated by ordinary differential equations, difference equations for, Cauchy and boundary value problems for differential equations, error estimation, stable and unstable difference schemes.
Weekly Schedule
1) Foundations of Matrix Analysis2) Principles of Numerical Mathematics
3) Direct Methods for the Solution of Linear Systems
4) Iterative Methods for Solving Linear Systems
5) Approximation of Eigenvalues and Eigenvectors
6) Root?nding for Nonlinear Equations
7) Nonlinear Systems and Numerical Optimization
8) Midterm examination/Assessment
9) Polynomial Interpolation
10) Orthogonal Polynomials in Approximation Theory
11) Numerical Solution of Ordinary Di?erential Equations
12) Boundary Value Problems
13) Boundary Value Problems
14) Parabolic and Hyperbolic Initial Boundary Value Problems
15) Parabolic and Hyperbolic Initial Boundary Value Problems
16) Final examination
Recommended or Required Reading
1- Numerical Mathematics, Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
2- Applied numerical methods, Brice Carnahan, H. A. Luther, James O. Wilkes
3- Applied Numerical Methods, Steven Chapra
4- Applied Numerical Methods, A. Gourdin, M. Boumahrat
5- Applied numerical methods using MATLAB, Won-yong Yang
6- Applied numerical methods for engineers, Terrence J. Akai
7- Applied Numerical Methods for Engineers and Scientists, S. S. Rao
8- Numerical analysis, Richard L. Burden, J. Douglas Faires
9- Applied numerical methods for digital computation, Merlin L. James, Gerald M. Smith, J. C. Wolford
10- Applied numerical methods for engineers using MATLAB and C, Robert Joseph Schilling, Sandra L. Harris
11- Applied Functional Analysis:
Numerical Methods, Wavelet Methods, and Image Processing, Abul Hasan Siddiqi
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Planned Learning Activities and Teaching Methods
1) Lecture
2) Discussion
3) Demonstration
4) Group Study
5) Problem Solving
Assessment Methods and Criteria
Contribution of Quiz to Course Grade |
70% |
|---|---|
Contribution of Final Examination to Course Grade |
30% |
Total |
100% |
Language of Instruction
Turkish
Work Placement(s)
Not Required