BPM_NUME Numerical Methods

Faculty of Economics and Administration
Spring 2016
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
Supplier department: Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration
Timetable
Tue 10:15–11:00 S310
  • Timetable of Seminar Groups:
BPM_NUME/01: Tue 8:30–10:05 S310, V. Studený
Prerequisites
( BPM_MATE Mathematics ) && ! BPM_NUMA Numerical methods && !NOWANY( BPM_NUMA 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
  • Hausdorff dimnsion. Hurst coefficient. Flat tailed distributions. Quantitative analysisi of rates of financial actives. Noah an Joseph efect. Selfsimilarity, chaos and power law. 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
  • MANDELBROT, Benoît B. Fractals and chaos : the Mandelbrot set and beyond : selecta volume C. New York: Springer, 2004, xii, 308. ISBN 0387201580. info
  • MANDELBROT, Benoît B. and Richard L. HUDSON. The (mis)behavior of markets : a fractal view of financial turbulence. New York: Basic books, 2004, xxx, 328. ISBN 0465043577. info
  • MANDELBROT, Benoît B. Fractals and scaling in finance : discontinuity, concentration, risk. New York: Springer, 1997, x, 551. ISBN 0387983635. info
  • MANDELBROT, Benoît B. Die fraktale Geometrie der Natur. Basel: Birkhäuser Verlag, 1987, 491 s. ISBN 376431771X. info
  • MANDELBROT, Benoit B. Die fraktale Geometrie der Natur. Basel: Birkhäuser Verlag, 1987, 491 s. ISBN 3-7643-1771-X. info
  • MANDELBROT, Benoit B. The fractal geometry of nature. Update and augmented. New York: W.H. Freeman, 1983, 468 s. ISBN 0-7167-1186-9. info
Teaching methods
Lectures, class discussion, group projects, homeworks
Assessment methods
Test, project, oral exam
Language of instruction
English
Further comments (probably available only in Czech)
The course is taught annually.
Information about innovation of course.
This course has been innovated under the project "Inovace studia ekonomických disciplín v souladu s požadavky znalostní ekonomiky (CZ.1.07/2.2.00/28.0227)" which is cofinanced by the European Social Fond and the national budget of the Czech Republic.

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The course is also listed under the following terms Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015.
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