PMNUMA Numerical Methods

Faculty of Economics and Administration
Spring 2009
Extent and Intensity
1/2/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Václav Studený, Ph.D. (lecturer)
RNDr. Václav Studený, Ph.D. (seminar tutor)
Guaranteed by
prof. Ing. Osvald Vašíček, CSc.
Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration
Contact Person: Mgr. Jana Nesvadbová
Timetable
Thu 15:30–17:05 S313
Prerequisites
Basic of mathematical analysis, algebra, linear algebra
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.

The capacity limit for the course is 24 student(s).
Current registration and enrolment status: enrolled: 0/24, only registered: 0/24
fields of study / plans the course is directly associated with
Course objectives
Numerické metody Pojetí předmětu je motivováno snahou ukázat studentům možnosti zpracování empirických dat numericky, například metodami aproximace a zlepšit schopnost studentů řešit problémy matematické povahy počítačem, a zprostředkovat jim osobní zkušenost s některými matematickými objekty. Tuto zkušenost poté doplnit teoretickým základem, který ji zobecní z pozorovaného příkladu na třídu příkladů. Jsou studována především dvě témata: aproximace funkce (kvalita různých aproximací je pak na konkrétních příkladech porovnávána v různých metrikách) a řešení nelineárních rovnic.
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 ion different metrics. -Projection onto a space of function by minimizing the least-squares error. -Nonlinear equation --Horner formula --Regula falsi -Fixpoints of contractions.
Literature
  • Mario J. Miranda and Paul L. Fackler, Applied Computational Economics and Finance, ISBN-10: 0-262-13420-9, ISBN-13: 978-0-262-13420-0
  • Kenneth L. Judd: Numerical Methods in Economics, ISBN-10: 0-262-10071-1, ISBN-13: 978-0-262-10071-7
  • Sheskin, David J., Handbook of Parametric and Nonparametric Statistical Procedures, CRC Press, 1997
Assessment methods
tests, pojects, oral exam
Language of instruction
English
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2007, Spring 2008.
  • Enrolment Statistics (recent)
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