Syllabus
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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
Annotation
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.