| Course Type | Elective Course |
|---|
| Course Level | Bachelor's Degree |
|---|
| Year of Study | - |
|---|
| Semester | - |
|---|
| ECTS | 4 |
|---|
| Name of Lecturer(s) |
- |
| Learning Outcomes |
At the end of this course, the students;
- Approximate functions using Taylor polynomials, calculate upper bounds for error
- Will be able to perform polynomial interpolation for curve fitting using Lagrange polynomials.
- Solve the equation f(x)=0 using the interval halving algorithm.
|
| Mode of Delivery | Face to face |
|---|
| Prerequisites | No |
|---|
| Recommended Optional Programme Components | Analysis |
|---|
| Course Description | The course content includes the following topics: the concept of error, definitions of absolute and relative error; solutions of nonlinear equations, halving method, newton's method, chord method, fixed points and functional iteration, solutions of systems of linear equations, matrix algebra, gauss elimination method, pivoting, LU factorization; function approximations, polynomial interpolation, divided differences, taylor approximation, least squares method |
|---|
| Course Contents |
| WEEK |
TOPICS |
|
1st Week |
Mathematical prerequisites: limits, continuity, differentiability |
|
2nd Week |
Taylor series |
|
3rd Week |
Difference equations |
|
4th Week |
Computer arithmetic, error analysis |
|
5th Week |
Finding equation roots; bisection method |
|
6th Week |
Newton's method, secant method |
|
7th Week |
Fixed point solutions |
|
8th Week |
Midterm |
|
9th Week |
Polynomial interpolation |
|
10th Week |
Taylor polynomials, divided differences |
|
11th Week |
Taylor polynomials, divided differences |
|
12th Week |
Hermite interpolation |
|
13th Week |
Hermite interpolation |
|
14th Week |
Least squares method |
|
15th Week |
General review |
|
| Recommended or Required Reading | Cheney,W.,-Kincaid,D., Numerical Mathematics and Computing,Brooks,1985
Cheney,W.,-Kincaid,D., (Tercüme) Nümerik Analiz, Gazi Kitabevi Yayınları, 2011
Yakowitz,S., An Introduction to Numerical Computations, Macmillan, 1989 |
|---|
| Planned Learning Activities and Teaching Methods |
- Lecture
- Questions/Answers
|
|---|
| Assessment Methods and Criteria |
|
Quantity |
Percentage (%) |
| Mid-term |
1 |
40 |
| Quiz |
2 |
10 |
| Total(%) |
|
50 |
| Contribution of In-term Studies to Overall Grade(%) |
|
50 |
| Contribution of Final Examination to Overall Grade(%) |
|
50 |
| Total(%) |
|
100 |
|
| ECTS Allocated Based on Student Workload |
| Activities |
Quantity |
Duration (Hour) |
Total Workload (Hour) |
| Midterm exam |
1 |
2 |
2 |
| Preparation for Quiz |
2 |
4 |
8 |
| Individual or group work |
13 |
2 |
26 |
| Preparation for Final exam |
1 |
28 |
28 |
| Course hours |
13 |
3 |
39 |
| Preparation for Midterm exam |
1 |
15 |
15 |
| Laboratory (including preparation) |
|
|
|
| Final exam |
1 |
2 |
2 |
| Homework |
|
|
|
| Total Work Load | 120 |
| Total Work Load / 30 (h) | 4 |
| ECTS Credit of the Course | 4 |
|
| Language of Instruction | Turkish |
|---|
| Work Placement(s) | No |
|---|
