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| COM3009 | Numerical Analysis | 3+0+0 | ECTS:5 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of COMPUTER ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Doç. Dr. Hüseyin PEHLİVAN | | Co-Lecturer | None | | Language of instruction | | | Professional practise ( internship ) | None | | | | The aim of the course: | | The course aims to give an introduction of some advanced methods of numerical analysis, including fundamental algorithms for solving nonlinear equations and systems of linear equations, function approximation methods, curve fitting methods, numerical differentiation and integration methods, ordinary differential equations, eigenvalues and eigenvectors. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | numerically solve nonlinear equations of any order. | 1,2 | 1, | | LO - 2 : | solve any system of linear equations. | 1,2 | 1, | | LO - 3 : | find polynomial functions to numerically approximate any kind of functions. | 1,2 | 1, | | LO - 4 : | find numerical approximations to the derivatives and integrals of functions. | 1,2 | 1, | | LO - 5 : | numerically solve a small class of ordinary differential equations. | 1,2 | 1, | | LO - 6 : | calculate eigenvalues and eigenvectors of a square matrix. | 1,2 | 1, | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome | | |
| Solution of nonlinear equations f(x) = 0: Fixed point iteration, bisection method, false position or regula falsi method, Newton-Raphson method, Secant method, Halley's Method, nonlinear systems. Solution of linear systems AX = B: Back substitution and forward substitution, Gauss-Jordan elimination and pivoting, inverse matrix, LU factorization, Jacobi and Gauss-Seidel iteration, row reduced echelon form, linear programming-Simplex method. Maclaurin and Taylor series: Lagrange polynomial interpolation and approximation, Newton interpolation polynomial, Hermite polynomial interpolation, cubic splines, Pade approximation. Curve fitting: Least squares polynomials, nonlinear curve fitting, logistic curve, FFT and trigonometric polynomials, conic fit, circle of curvature. Numerical differentiation: Richardson extrapolation, derivation of numerical differentiation formulas. Numerical integration: Riemann sums, Midpoint Rule, trapezoidal rule, Simpson's rule, Simpson's 3/8 rule, Boole's rule, Monte Carlo Integration. Solution of differential equations: Euler's method, Taylor series method, Runge-Kutta method, finite difference method, Frobenius series solution, Picard iteration. Eigenvalues and Eigenvectors: Power method, compartment model, matrix exponential.
Numerical Optimization: Golden ratio search, Fibonacci search, Newton's search method.
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | General Introduction and Concepts | | | Week 2 | The Solution of Nonlinear Equations - I | | | Week 3 | The Solution of Nonlinear Equations - II | | | Week 4 | The Solution of Linear Systems | | | Week 5 | The Solution of Nonlinear Systems | | | Week 6 | Interpolation | | | Week 7 | Polynomial Approximation | | | Week 8 | Curve Fitting | | | Week 9 | Mid-term exam | | | Week 10 | Numerical Differentiation and Richardson Extrapolation | | | Week 11 | Numerical Integration | | | Week 12 | Multiple Numerical Integration | | | Week 13 | Solution of Differential Equations | | | Week 14 | Eigenvalues and Eigenvectors | | | Week 15 | Numerical Optimization | | | Week 16 | End-of-term exam | | | |
| 1 | Chapra, S. C., 2017, Applied Numerical Methods with MATLAB for Engineers and Scientists, 4th ed. McGraw-Hill Education, 720 p. | | | |
| 1 | Gilat, A., Subramaniam, V., 2013, Numerical Methods for Engineers and Scientists: An introduction with applications using MATLAB, 3rd ed., Wiley, 576 p. | | | 2 | Burden, R. L., Faires, J. D., 2010, Numerical Analysis, 9th ed., Brooks/Cole, 895 p. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | | 2 | 50 | | End-of-term exam | 16 | | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 2 | 4 | 8 | | Arasınav için hazırlık | 8 | 1 | 8 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 15 | 1 | 15 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 77 |
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