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Numerical methods - basic terminology, evaluation of functions, approximation, root finding, integration of functions, solution of linear algebraic equations, integration of ordinary differential equations, partial differential equations. Designated for doctoral and master study.
Last update: T_KEVF (16.05.2005)
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Students will learn basic numerical algorithms (see annotation and syllabus). Last update: IBARVIK/MFF.CUNI.CZ (16.05.2008)
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Successful passing of the exam is a condition for completing the course. Last update: Barvík Ivan, RNDr., Ph.D. (30.10.2019)
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Ralston A.: Základy numerické matematiky, Academia, Praha 1978. Press W.H. et al.: Numerical Recipes in FORTRAN (Pascal, C), Cambridge University Press, Cambridge 1992. Vicher M.: Numerická matematika, skripta, PF UJEP, Ústí nad Labem 2003. Last update: T_KEVF (05.05.2010)
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Lectures and practical exercises in computer lab Last update: IBARVIK/MFF.CUNI.CZ (16.05.2008)
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Zkouška je ústní a student dostává otázky dle sylabu předmětu v rozsahu, který byl prezentován na přednáškách. Last update: Pavlů Jiří, doc. RNDr., Ph.D. (14.06.2019)
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1. Numerical mathematics
Representation of numbers, accuracy, errors. 2. Interpolation and approximation Interpolation. Least square aproximation, Čebyšev aproximation, spline functions. 3. Numerical integration and differentiation Formulae for equally spaced abscissas. Gaussian quadrature. Numerical differentiation. 4. Solution of linear algebraic equations Gauss elimination and Gauss-Jordan elimination. Iterative methods. Matrix operations. 5. Root finding and solution of nenlinear sets of equations 6. Integration of ordinary differential equations Euler method. Runge-Kutta methods. Predictor-corrector methods. Errors. 7. Solution of partial differential equations Diference equations. Relaxation method. Over-relaxation methods and further techniques for the increase of convergency. Solution of hyperbolic equations. 8. Application of Monte Carlo method in numerical mathematics Last update: T_KEVF (16.05.2005)
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