Numerical Methods and Algorithms 390-FG1-2MNA
Topics covered in lectures and laboratory classes:
Numerical Analysis: finding zeros of a function of one variable (secant method, bisection method, Newton–Raphson method, comparison of algorithms, error analysis), numerical integration (Newton–Cotes quadratures, Gaussian quadratures), minima of functions of many variables (conjugate directions method, conjugate gradient method, annealing method), ordinary differential equations (Euler method, multistep methods, implicit methods, leapfrog method, Runge–Kutta method, algorithm stability), partial differential equations (elliptic equations – relaxation method, hyperbolic equations – Lax method, parabolic equations – Crank–Nicolson method, stability of algorithms), integral equations.
Numerical Linear Algebra: solving systems of linear equations (Gauss–Jordan elimination method, LU decomposition (Crout algorithm), iterative methods), systems of nonlinear equations (iterative methods), eigenvalues and eigenvectors (Jacobi method for symmetric matrices).
Computational Probability: generators of pseudorandom numbers with uniform distribution, Monte Carlo quadrature, construction of pseudorandom number generators with distributions other than uniform (von Neumann and Metropolis algorithms), Monte Carlo method.
Fast Fourier Transform: differentiation, integration (convolution, correlation), solving partial differential equations (split-operator method).
Type of course
Course coordinators
Learning outcomes
Student
KP6_WG4 knows advanced computational methods used to solve typical physical problems and examples of the practical implementation of such methods using appropriate IT tools; has knowledge of programming and software engineering within the scope specified in the curriculum.
KP6_UW4 is able to apply numerical methods to solve mathematical problems; has the ability to use basic software packages and selected programming languages within the scope defined in the curriculum.
KP6_UK5 is able to carry out a critical analysis of the results of measurements, observations, or theoretical calculations, together with a quantitative assessment of the accuracy of the results.
KP6_KO2 is ready to consult scientific and popular science literature in order to deepen and broaden knowledge, taking into account the risks associated with obtaining information from unverified sources, including the Internet.
Assessment criteria
Lecture: After completing the course Numerical Methods and Algorithms, an exam is held that consists of assessing practical skills in implementing the algorithms discussed during the course.
Bibliography
Basic:
Numerical Recipes – W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery
Computational Physics – D. Potter
Numerical Analysis – D. Kincaid, W. Cheney
Supplementary:
Computational Physics – S.E. Koonin
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: