SylabUZ
| Course name | Numerical methods |
| Course ID | 13.2-WF-FiAP-NM-S17 |
| Faculty | Faculty of Physics and Astronomy |
| Field of study | Physics |
| Education profile | academic |
| Level of studies | First-cycle studies leading to Bachelor's degree |
| Beginning semester | winter term 2020/2021 |
| Semester | 2 |
| ECTS credits to win | 4 |
| Available in specialities | Computer Physics |
| Course type | obligatory |
| Teaching language | english |
| Author of syllabus |
|
| The class form | Hours per semester (full-time) | Hours per week (full-time) | Hours per semester (part-time) | Hours per week (part-time) | Form of assignment |
| Lecture | 30 | 2 | - | - | Exam |
| Laboratory | 30 | 2 | - | - | Credit with grade |
Understanding the basics of Numerical Methods.
Knowledge of the linear algebra and calculus. Ability to program in C or another programming language at the level sufficient to solve problems.
Lecture:
The accuracy of the calculations and the types of errors.
Bisection method, secant and Newton's method - approximate root-finding algorithms.
Matrices. Gaussian elimination algorithm, LU decomposition. Inverse matrix. Determinants.
Eigenvalues and eigenvectors, QR method.
Polynomial interpolation, Lagrange's and Newton's method. Spline functions.
Numerical integration, the trapezoidal and Simpson's method. Gaussian quadrature.
Numerical differentiation.
Fast Fourier Transform.
Laboratory:
Searching for roots of the nonanalytical functions by bisection and Newton's method.
Finding the solution of linear equations.
Calculating the integrals using Simpson's method with a given accuracy.
The use of spline functions to the approximate calculation of definite integrals.
Calculations of nodes and weights for Gaussian quadrature.
Conventional lecture, presentation. Laboratory exercises in the computer lab.
| Outcome description | Outcome symbols | Methods of verification | The class form |
The condition of positive assessment of the lecture is taking the final test and obtain at least 51% of points.
The pass for the laboratory is to perform all programming exercises.
Before taking the exam a student must obtain a pass from the laboratory.
Final mark: a weighted average rating of the exam (60%) and laboratory (40%).
[1] Z. Fortuna, B. Macukow, J. Wąsoski, Metody numeryczne, WNT, Warszawa 1998.
[2] A. Bjorck, G. Dahlquist, Metody numeryczne, PWN, Warszawa 1987.
[3] A. Ralston, Wstęp do analizy numerycznej, WNT, Warszawa 1975.
[4] J. i M. Jankowscy, Przegląd metod i algorytmów numerycznych, WNT, Warszawa 1981.
[5] W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Reciepies in C, CUP,
1992.
Modified by dr hab. Piotr Lubiński, prof. UZ (last modification: 03-06-2020 15:58)
