F6150 Advanced numerical methods

Faculty of Science
Spring 2009
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: graded credit.
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Josef Humlíček, CSc.
Timetable
Thu 15:00–16:50 Fs1 6/1017, Thu 17:00–17:50 Fs1 6/1017
Prerequisites (in Czech)
F5330 Basic numerical methods
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
Course objectives
During the semester students obtain basic knowledge on themes: Interpolation and aproximation, numerical quadrature,multidimensional minimization and nonlinear regression, initial-value and boundary-value problems for ODEs,introduction to solving PDEs, fast Fourier transform.
Syllabus
  • 1. Polynomial interpolation and aproximation.
  • 2. Cubic interpolation spline.
  • 3. Data smoothing,smoothing spline.
  • 4. Numerical differentiation.
  • 5. Numerical quadrature: Newton-Cotes methods, Richardson extrapolation and Romberg quadrature, Gauss methods.
  • 6. Minimization of functions.
  • 7. Multidimensional optimization, nonlinear regression.
  • 8. Initial-value problem for ordinary differential equations: Runge-Kutta methods, multistep methods. 9. Boundary-value problem for ordinary differential equations. 10. Introduction to numerical solution of partial differential equations: heat equation in 1D, Laplace problem in 2D.
  • 11. Discrete Fourier transform, fast Fourier transform.
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Assessment methods
Lecture + individual work on PC. Demands for graded credit: have a good knowledge of topics presented in the lecture together with solid results of individual work during the semester.
Language of instruction
Czech
Further Comments
The course is taught annually.
Teacher's information
http://monoceros.physics.muni.cz/~jancely
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2009, recent)
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