Short review of GNU/LINUX operating system, Matlab and Fortran, errors in numerical computing (error types and floating point arithmetic), evaluation of polynomials and their derivatives, summation of series, recursions, nonlinear equations (methods of bracketing, secant and Newton), approximations of functions (polynomial interpolation, Chebishev and Fourier approximation), least squares method, orthogonal bases, global and local smoothing, numerical differentiation, numerical integration (Newton-Cotes and Gauss formulae), basics of numerical linear algebra (systems of linear equations, matrix condition number, basics of perturbation theory).
LEARNING OUTCOMES:
Students will be able to:
state basic features of the GNU/Linux operating system, of Matlab computing system and Fortran programing language
use Linux, Matlab and Fortran at primary level
explain and compare the round-off error and truncation error
evaluate polynomial and sum of function series and identify problems that can affect the calculation
apply least square method to approximation of functions
calculate numerically derivative and integral and provide the error estimate
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- Z. Drmač, M. Marušić, M. Rogina, S. Singer, S. Singer: Numerička analiza, skripta na Internetu, 2003/2004.
- J. H. Mathews, K. D. Fink: Numerical Methods using Matlab, Prentice Hall, New Jersey, 2004.
- W. H. Press , S. A. Teukolsky , W. T. Vetterling , B. P. Flannery: Numerical Recipes in Fortran 90, electronic edition (http://www.nrbook.com/nr3/).
- M. Metcalf, J. Reid: FORTRAN 90/95 Explained, Oxford Univ. Press, 1999.
- T. M. R. Ellis, I. R. Philips, T. M. Lahey: Fortran 90 Programming, Addison-Wesley, 1996.
- Z. Kalafatić, A. Pošćić, S. Šegvić, j. Šribar: Python za znatiželjne, Element, 2016.
- Gaël Varoquaux i dr.: Scipy, Lecture Notes, www.scipy-lectures.org, 2017.
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