Week. Lecture
-------------
1st Course contents, the issue of errors, stability of calculations.
2nd Solution of nonlinear equations, separation of roots, the simplest methods.
3rd Newton's method and fixed-point iterations.
4th Direct methods for solving linear equations, Gaussian elimination and LU-decomposition.
5th Eigenvalues and eigenvectors, numerical calculation.
6th Iterative methods for solving linear equations.
7th Interpolation by polynomials and splines.
8th Least squares approximation.
9th Numerical differentiation and integration.
10th Extrapolation in the calculation of integrals. Gaussian integration formulas.
11th One-step methods for solving initial value problems for ordinary differential equations.
12th Multistep methods.
13th Ordinary differential equations of higher order.
14th Systems of differential equations.
Program of tutorials
====================
Week. Tutorial
--------------
1st Introduction to mathematical software.
2nd Separation of roots, the simplest iterative methods.
3rd Newton's method and fixed-point iterations.
4th Systems of nonlinear equations.
5th 1st examination. Calculation of LU-decomposition.
6th Application of LU-decomposition.
7th Iterative methods for solving linear systems.
8th Elementary, Lagrange and Newton interpolation polynomials.
9th 2nd examination. Interpolation by splines.
10th Least squares approximation.
11th The numerical calculation of integrals, extrapolation.
12th One-step methods for solving differential equations.
13th 3rd examination. Multistep methods.
14th Credits.
-------------
1st Course contents, the issue of errors, stability of calculations.
2nd Solution of nonlinear equations, separation of roots, the simplest methods.
3rd Newton's method and fixed-point iterations.
4th Direct methods for solving linear equations, Gaussian elimination and LU-decomposition.
5th Eigenvalues and eigenvectors, numerical calculation.
6th Iterative methods for solving linear equations.
7th Interpolation by polynomials and splines.
8th Least squares approximation.
9th Numerical differentiation and integration.
10th Extrapolation in the calculation of integrals. Gaussian integration formulas.
11th One-step methods for solving initial value problems for ordinary differential equations.
12th Multistep methods.
13th Ordinary differential equations of higher order.
14th Systems of differential equations.
Program of tutorials
====================
Week. Tutorial
--------------
1st Introduction to mathematical software.
2nd Separation of roots, the simplest iterative methods.
3rd Newton's method and fixed-point iterations.
4th Systems of nonlinear equations.
5th 1st examination. Calculation of LU-decomposition.
6th Application of LU-decomposition.
7th Iterative methods for solving linear systems.
8th Elementary, Lagrange and Newton interpolation polynomials.
9th 2nd examination. Interpolation by splines.
10th Least squares approximation.
11th The numerical calculation of integrals, extrapolation.
12th One-step methods for solving differential equations.
13th 3rd examination. Multistep methods.
14th Credits.