BPM_NUME Numerical Methods

Faculty of Economics and Administration
Spring 2010
Extent and Intensity
1/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Václav Studený, Ph.D. (lecturer)
RNDr. Václav Studený, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Luboš Bauer, CSc.
Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration
Contact Person: Lenka Hráčková
Timetable
Tue 9:20–10:05 S310
  • Timetable of Seminar Groups:
BPM_NUME/01: Tue 7:40–9:15 S310, V. Studený
Prerequisites
(( PMMAT2 Mathematics II || PMZMII Introduction to Mathematics II || PMMAT_E Mathematics - E || BPM_MATE Mathematics )) && ((! PMNUME Numerical Methods ) || (! PMNUMA Numerical Methods ))
Basics of mathematical analysis, algebra, linear algebra.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
At the end of the course students should be able to:
- execute numerical processing of empirical data;
- solve mathematical problem using the computer;
- use appropriate stochastic tools for morphology of amorphous processes.
Syllabus
  • Metric spaces and linear spaces with scalar product
  • - Metric on spaces of functions
  • - Ortonormal basis and projections
  • Polynomial interpolation
  • - Lagrange polynomial
  • - Newton form of the interpolation polynomial
  • - Bernstein form of the interpolation polynomial
  • - Newton–Cotes formulas
  • - Taylor series expansion
  • - Hermite interpolation, (interpolation using the unique polynomial of degree at most 2n-1 that takes prescribed function and first derivative values at n distinct points)
  • Fourier series decomposition of a periodic function into a sum of simple oscillating functions, namely sines and cosines
  • Fitting a model function that is linear in the model parameters to data by minimizing the least-squares error in different metrics
  • Projection onto a space of function by minimizing the least-squares error
  • Nonlinear equations
  • Horner formula
  • Regula falsi
  • Fixpoints of contractions
  • Stochastics models
Literature
  • HOROVÁ, Ivana. Numerické metody. 1st ed. Brno: Masarykova univerzita, 1999, 230 pp. ISBN 80-210-2202-7. info
  • MATHEWS, John H. Numerical methods for mathematics, science and engineering. 2nd ed. Englewood Cliffs: Prentice-Hall International, 1992, 646 pp. X. ISBN 0-13-625047-5. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • REKTORYS, Karel. Přehled užité matematiky. 4. nezm. vyd. Praha: Státní nakladatelství technické literatury, 1981, 1139 s. info
Teaching methods
Lectures, class discussion, group projects, homeworks
Assessment methods
Test, project, oral exam
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
General note: Nezapisují si studenti, kteří absolvovali předměty PMNUME nebo PMNUMA.
The course is also listed under the following terms Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016.
  • Enrolment Statistics (Spring 2010, recent)
  • Permalink: https://is.muni.cz/course/econ/spring2010/BPM_NUME