Numerical Methods
Informacje ogólne
Kod przedmiotu: | 0900-ERS-3MNU |
Kod Erasmus / ISCED: |
11.103
|
Nazwa przedmiotu: | Numerical Methods |
Jednostka: | Wydział Fizyki. (do 30.09.2019) |
Grupy: | |
Punkty ECTS i inne: |
(brak)
|
Język prowadzenia: | angielski |
Rodzaj przedmiotu: | fakultatywne |
Skrócony opis: |
The aim of the lectures is to make students familiar with the basics of numerical calculus, numerical algebra, and numerical probability. |
Pełny opis: |
Numerical calculus: root finding (secant method, bisection, Newton-Raphson method), numerical integration (Newton-Cotes formulas, Gaussian quadratures), minimization of functions (conjugate directions method, conjugate gradient method, annealing method), integration of ordinary differential equations (Euler method, multistep and implicit methods, leapfrog method, Runge-Kutta method, stability and acuracy of difference schemes), partial differential equations (elliptic equations – relaxation method, hyperbolic equations – Lax scheme, parabolic equations – Crank-Nicholson scheme, stability analysis), integral equations. Numerical algebra: solving set of linear equations (Gauss-Jordan elimination, LU decomposition (Crout method), iterative methods), nonlinear set of equations (iterative methods), eigenvalues and eigenvectors (Jacobi method for a symmetric matrix). Numerical probability: uniformly distributed pseudo-random numbers, Monte Carlo quadrature, pseudo-random number generators for any distribution (von Neumann and Metropolis algorithms), Monte Carlo method. Fast Fourier Transform: differentiating, integrating (convolution, correlation), and solving partial differential equations (split operator method). |
Literatura: |
W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes D. Potter, Computational Physics D. Kincaid, W. Cheney, Numerical Abalysis. Mathematics of Scientific Computing S. E. Koonin, Computational Physics |
Metody i kryteria oceniania: |
At the end of the course there is an exam. It is supposed to measure how well a student understands the subjects trained during the lectures. The student will be using a computer to write his/her exam. |
Właścicielem praw autorskich jest Uniwersytet w Białymstoku.