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Description of Individual Course Units| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | AYA215.2B | Numerical methods | Elective | 2 | 3 | 4 |
| | Level of Course Unit | | First Cycle | | Objectives of the Course | | The aim of this course is to give the students the ability to solve problems numerically, to teach the applications and applications in computer environment by introducing numerical methods used in problem solving, | | Name of Lecturer(s) | | Dr. Öğr. Üyesi Sinan KUL | | Learning Outcomes | | 1 | Explains the main logic of the numerical methods. | | 2 | Solves problems by using the gained knowledge from this course. | | 3 | Defines and applies the appropriate numerical method for any engineering problem. | | 4 | Analyzes linear equation systems. | | 5 | Calculates numerical differentiation and numerical integral. | | 6 | Obtains results by using different parameters in the numerical solutions and to distinguish the more correct result. |
| | Mode of Delivery | | Normal Education | | Prerequisites and co-requisities | | None | | Recommended Optional Programme Components | | None | | Course Contents | | 1 Approaches and errors, accuracy and precision, error definitions, rounding errors, total numerical error
2 Roots of algebraic equations, closed methods; Interval splitting method, linear interpolation method
3 Open methods; Newton-Raphson method, Secant method, multiple roots, programming and structural functions with root locating
4 Systems of linear equations, matrix form of systems of equations, matrix algebra, Solution methods; Gauss elimination method, Gauss-Seidel method, LU decomposition method, programming and structural functions of linear algebraic equation sets solution
5 Curve fitting, interpolation method with Newton's split differences table, Lagrange interpolation, structural functions with programming, curve fitting and polynomial regression
6 Numerical integration; The trapezoidal rule, Simpson rules, problems
7 Numerical differentiation; Numerical derivative with forward, backward and central differences
8 Numerical solutions of ordinary differential equations: Initial value problems; Euler and Runge Kutta Methods, initial value problems with programming
9 Solution of boundary value problems by finite difference method | | Weekly Detailed Course Contents | |
| 1 | Approaches and Errors, Accuracy and Precision, Error Definitions, Rounding Errors, Total Numerical Error | | | | 2 | Roots of Equilibrium; Interval Dividing Method, Linear Interpolation Method | | | | 3 | Open Methods; Newton Method, Secant Method, Multiple Roots Method, Root Finding Method with Programming | | | | 4 | Linear Equation Systems, Matrix Form of Equation Systems, Matrix Algebra, Analytical Solution Methods; Gaussian Elimination Method | | | | 5 | Iterative Solution Methods; Solution of Linear Algebraic Equations with Gauss-Seidel Method and Programming | | | | 6 | Solution of Non-linear Cebrik Equation Teeth: Newton Raphson Method | | | | 7 | Curve Fitting; Least Squares Method, Linear and Non-linear Regression | | | | 8 | Midterm Exam
| | | | 9 | Interpolation Method with Newton's Divided Differences Table, Lagrange Interpolation, Curve Fitting and Regression with Programming | | | | 10 | Numerical Integration; The Trapezoidal Rule, Simpson's Rule, Problems | | | | 11 | Numerical Derivative; Forward, Backward and Numerical Differential Differences | | | | 12 | Numerical Solutions of Ordinary Differential Equations; Initial Value Problems; Euler and Runge Kutta Methods | | | | 13 | Solution of Initial Value Problems with Programming, Stiff Problems | | | | 14 | Definition of Boundary Value Problems, Boundary Conditions, Finite Difference Method | | | | 15 | Solution of boundary value problems by finite difference method | | | | 16 | Final Exam | | |
| | Recommended or Required Reading | | 1 J. D. Faires and R. L. Burden, Numerical Methods, Brooks Cole, 2002.
2 L. F. Shampine, I. Gladwell, S. Thompson, Solving ODEs with MATLAB, Cambridge University Press, 2003. | | Planned Learning Activities and Teaching Methods | | | Assessment Methods and Criteria | |
| Midterm Examination | 1 | 100 | | SUM | 100 | |
| Final Examination | 1 | 100 | | SUM | 100 | | Term (or Year) Learning Activities | 40 | | End Of Term (or Year) Learning Activities | 60 | | SUM | 100 |
| | Language of Instruction | | Turkish | | Work Placement(s) | | None |
| | Workload Calculation | |
| Midterm Examination | 1 | 1 | 1 | | Final Examination | 1 | 1 | 1 | | Attending Lectures | 14 | 3 | 42 | | Self Study | 14 | 2 | 28 | | Individual Study for Mid term Examination | 7 | 2 | 14 | | Individual Study for Final Examination | 7 | 2 | 14 | | Homework | 1 | 5 | 5 | |
| Contribution of Learning Outcomes to Programme Outcomes | | LO1 | 4 | | | | | | | | | | LO2 | 5 | | | | | | | | | | LO3 | 5 | | | | | | | | | | LO4 | 3 | | | | | | | | | | LO5 | 5 | | | | | | | | | | LO6 | 4 | | | | | | | | |
| | * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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