M5180 Numerical Methods II

Faculty of Science
Autumn 2005
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Mgr. Jiří Zelinka, Dr. (seminar tutor)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Timetable
Thu 13:00–14:50 N21
  • Timetable of Seminar Groups:
M5180/01: Thu 8:00–8:50 M3,04005 - dříve Janáčkovo nám. 2a, J. Zelinka, Rozvrhově doporučeno pro 3. ročník Mo,Ms
M5180/02: Thu 9:00–9:50 M3,04005 - dříve Janáčkovo nám. 2a, J. Zelinka, Rozvrhově doporučeno pro FI
Prerequisites
M4180 Numerical methods I || ( FI:M028 Numerical Methods I )
Differential and inegral calculus of one and more variables. Basic knowledge of linear algebra.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 8 fields of study the course is directly associated with, display
Course objectives
This course together with the course Numerical methods I provides systematic explanation of numerical mathematics as the special scientific discipline.The course is focused on numerical methods of mathematical analysis,namely on inerpolation,numerical differen- tiation,numerical integration.Advantages and disadvantages of methods mentioned above are shown. In addition to the classical methods the modern procedures suitable for algorithmization and computer implementation are also presented.
Syllabus
  • Interpolation-Lagrange interpolation polynomial,Newton interpolation polynomial,the error of the polynomial interpolation,iterated inter- polation,Hermite interpolation polynomial,,cubic spline interpolation, general interpolation process. Least-squares method. Numerical differentiation-formulas based on a derivative of an interpolation polynomial,Richardson extrapolation. Numerical integration-quadrature formulas,degree of exactness and error,Gaussian quadratures,Lobatto quadrature,Newton-Cotes quadratures composite quadratures,inegrals with singularities,adaptive quadratures
Literature
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • HOROVÁ, Ivana. Numerické metody. 1st ed. Brno: Masarykova univerzita, 1999, 230 pp. ISBN 80-210-2202-7. info
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. 1. vyd. Praha: Nakladatelství technické literatury, 1985, 187 s. URL 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
  • BURDEN, Richard L. and Douglas J. FAIRES. Numerical analysis. 3rd ed. Boston: PWS Publishing Company, 1985, 676 pp. ISBN 0-87150-857-5. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • HOROVA, Ivana and Jiří ZELINKA. Numerické metody (Numerical Methods). 2nd ed. Brno: Masarykova univerzita v Brně, 2004, 294 pp. 3871/Př-2/04-17/31. ISBN 80-210-3317-7. info
Assessment methods (in Czech)
Výuka : přednáška, cvičení v počítačové učebně,podmínka pro udělení zápočtu-účast na cvičení,získání dostatečného počtu bodů z pisemek během semestru Zkouška:písemná a (ústní).
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2003, Autumn 2004, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2005, recent)
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