| Course Type | Elective Course |
|---|
| Course Level | Master's Degree Without Thesis |
|---|
| Year of Study | - |
|---|
| Semester | - |
|---|
| ECTS | 10 |
|---|
| Name of Lecturer(s) |
- |
| Learning Outcomes |
At the end of this course, the students;
- will have general information on basic numerical analysis.
|
| Mode of Delivery | Face to face |
|---|
| Prerequisites | No |
|---|
| Recommended Optional Programme Components | There is no recommended optional programme component for this course. |
|---|
| Course Description | Problems of NA, Linear Spaces, Linear Operators on Normed Spaces, Approximation Theory, Nonlinear Equations and Their Solution by Iteration, Finite Difference Method, Sobolev Spaces, Variational Formulations of Elliptic Boundary Value Problems, The Galerkin Method and Its Variants, Finite Element Analysis, Elliptic Variational Inequalities and Their Numerical Approximations, Numerical Solution of Fredholm Integral Equations of the Second Kind, Boundary Integral Equations |
|---|
| Course Contents |
| WEEK |
TOPICS |
|
1st Week |
Introduction,finite floating point arithmetic,catastrophic cancellation,chopping and rounding errors. |
|
2nd Week |
Solution of nonlinear equations;bisection method,secant method, Newton's method,fixed point iteration,Muller's method. |
|
3rd Week |
Numerical optimization;Method of goldensection search,Newton's method optimization. |
|
4th Week |
Solutions of linear algebraic equations. |
|
5th Week |
LU-decomposition,norms and errors. |
|
6th Week |
Condition numbers,iteration. |
|
7th Week |
Newton's method for systems , computer implementation. |
|
8th Week |
MIDTERM |
|
9th Week |
Interpoletion;Lagrange interpolation,Newton interpolation,inverse interpolation. |
|
10th Week |
Numerical Integration;trpezoidal rule Simpson's rule. |
|
11th Week |
Extrapolation , Gaussian quadrature. |
|
12th Week |
Numerical solution of ordinary differential equations. |
|
13th Week |
Euler's method, Runge-Kutta method, multi-step methods, |
|
14th Week |
Rates of conveges, global errors,algebric methods for boundary value problems,computer implementation. |
|
| Recommended or Required Reading | Applied Numerical Analysis,Addison ,C.F.Gerald and P. O. Wheatley , Addison Wesley,1994 |
|---|
| Planned Learning Activities and Teaching Methods |
- Lecture
- Questions/Answers
- Problem Solving
- Other
|
|---|
| Assessment Methods and Criteria |
|
Quantity |
Percentage (%) |
| Mid-term |
1 |
30 |
| Assignment |
1 |
10 |
| Project |
1 |
10 |
| Total(%) |
|
50 |
| Contribution of In-term Studies to Overall Grade(%) |
|
50 |
| Contribution of Final Examination to Overall Grade(%) |
|
50 |
| Total(%) |
|
100 |
|
| Language of Instruction | Turkish |
|---|
| Work Placement(s) | No |
|---|
