470-2501/03 – Numerical Methods (NM)
Gurantor department | Department of Applied Mathematics | Credits | 6 |
Subject guarantor | doc. Ing. Dalibor Lukáš, Ph.D. | Subject version guarantor | doc. Ing. Dalibor Lukáš, Ph.D. |
Study level | undergraduate or graduate | Requirement | Compulsory |
Year | 3 | Semester | winter |
| | Study language | Czech |
Year of introduction | 2019/2020 | Year of cancellation | |
Intended for the faculties | FEI | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
Numerical methods stands behind computer solutions to complex engineering problems. The course Numerical Methods 1 aims at helping students to choose a proper algorithm for the solution of selected problems of Calculus and analyze the solution regarding stability (sensitivity of the output data on the inputs) and computational complexity.
Teaching methods
Lectures
Tutorials
Project work
Summary
In this course numerical methods for selected problems of mathematical analysis are tought. We shall also prove convergence rates and present efficient implementation.
Compulsory literature:
- O. Steinbach, Numerische Mathematik 1. TU Graz, 2005. https://www.numerik.math.tugraz.at/berichte/Bericht0105.pdf
- A. Quarteroni, R. Sacco, F. Saleri, Numerical Mathematics. Springer, 2007. ISBN 0939-2475
Recommended literature:
Way of continuous check of knowledge in the course of semester
Test (10 pts.)
Project (20 pts.)
Written exam
E-learning
Other requirements
Successful defense of a semestral project.
Students are familiar with fundamentals of differential and integral calculus in 1 dimension.
Prerequisities
Co-requisities
Subject has no co-requisities.
Subject syllabus:
I. Data fitting: Lagrange interpolation, Chebyshev interpolation, least squares approximation, polynomial regression, orthogonal systems of polynomials (Legendre, Laguerre, Hermite), fast Fourier transform.
II. Numerical integration: Newton-Cotes quadrature, Gauss quadrature (Gauss-Legendre, Gauss-Laguerre, Gauss-Hermite).
III. Iterative methods for solution of nonlinear equations: bisection, fixed-point iterations, Newton method.
IV. Numerical solution to ordinary differential equations: one-step Euler, Crank-Nicholson, and Runge-Kutta methods, multi-step methods, predictor-corrector methods, Galerkin methods, parareal methods.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction