Numerical Methods Field of study: Physics
Programme code: W4-S2FZA22.2.2021

Module name: Numerical Methods
Module code: W4-2F-13-11
Programme code: W4-S2FZA22.2.2021
Semester: winter semester 2021/2022
Language of instruction: English
Form of verification: exam
ECTS credits: 4
Description:
The lecture will present the basics of programming in scientific applications and basic methods in the following issues: - numerical differentiation; - numerical integration (including adaptive scheme and Monte Carlo method); - numerical solving of nonlinear equations (bisection, Newton-Raphson method); - numerical solving of differential equations (Euler and Runge-Kutta methods, schemes used in MD); - matrix calculations (diagonalization, solving systems of linear equations). Multivariate minimization methods and numerical solving of N-body problem, as well as parallel computations, program optimization and use of numerical libraries will also be discussed. During the laboratory classes the student: - learns the basics of using the Linux environment; - learns how to compile and run programs; - learns how to analyze and present the obtained results (including creating plots); - implements numerical methods and studies their properties; - compares the usage of different numerical methods to solve the same problem; - uses computational methods to solve physical problems. Part of the time is devoted to discussing the algorithm for solving a given problem, the rest of it students spend at the computers, implementing and testing selected numerical methods. As part of his/her own work, the student gains experience by writing and running programs independently and consolidate acquired knowledge by reading suggested literature. Assessment is based on reports written by students after completing each laboratory assignment and oral exam.
Prerequisites:
Ability to program in any language that allows procedural programming (C/C++ recommended). Basic knowledge of mathematical analysis (differentiation and integration) and linear algebra.
Key reading:
[1] Tao Pang, An Introduction to Computational Physics, Cabridge University Press, Cambridge 2006 (CINiBA). [2] Forman Acton, Numerical Methods that Work, Harper and Row, New York 1970 (CINiBA).
Learning outcome of the module Codes of the learning outcomes of the programme to which the learning outcome of the module is related [level of competence: scale 1-5]
knows the basics of computational and IT techniques, supporting work of a physicist and understands their limitations [2F_11_1]
 KF_W07 [5/5]
knows the mathematical formalism useful in the construction and analysis of models physical of medium complexity; understands the consequences of using approximate methods [2F_11_2]
 KF_W06 [2/5]
knows how to use a mathematical apparatus to solve problems of medium complexity [2F_11_3]
 KF_U02 [3/5]
Type Description Codes of the learning outcomes of the module to which assessment is related
colloquium [2F_11_w_1]
Four times a semester; the tasks consist in writing several programs using the known numerical methods
 2F_11_1 2F_11_2 2F_11_3
written exam (at the computer) [2F_11_w_2]
The condition for taking the exam is passing the laboratory classes; scope of the material - all issues discussed during the lectures; grading scale 2-5;
 2F_11_1 2F_11_2 2F_11_3
Form of teaching Student's own work Assessment of the learning outcomes
Type Description (including teaching methods) Number of hours Description Number of hours
lecture [2F_11_fs_1]
discussion of the issues that are the subject of the lecture with the use of multimedia presentations and "live" illustrations of the operation of programs. Lecture materials available on the e-learning platform.
 10
Getting familiar with the materials posted on the e-learning platform and lecture notes; work with the textbook
 30 colloquium [2F_11_w_1] written exam (at the computer) [2F_11_w_2]
laboratory classes [2F_11_fs_2]
independent writing and running of computer programs; discussion at the blackboard: methods of approaching specific physical problems, algorithmization of the problem and emerging problems.
 30
Solving tasks (writing programs) placed on the e-learning platform,
 30 colloquium [2F_11_w_1]
Attachments
Module description (PDF)
Information concerning module syllabuses might be changed during studies.
Syllabuses (USOSweb)
Semester Module Language of instruction
(no information given)