- Course contents, the issue of errors, stability of calculations.
- Solution of nonlinear equations, separation of roots, the simplest methods.
- Newton's method and fixed-point iterations.
- Direct methods for solving linear equations, Gaussian elimination and LU-decomposition.
- Eigenvalues and eigenvectors, numerical calculation.
- Iterative methods for solving linear equations.
- Interpolation by polynomials and splines.
- Least squares approximation.
- Numerical differentiation and integration.
- Extrapolation in the calculation of integrals. Gaussian integration formulas.
- One-step methods for solving initial value problems for ordinary differential equations.
- Multistep methods.
- Ordinary differential equations of higher order.
- Systems of differential equations.
- Solution of nonlinear equations, separation of roots, the simplest methods.
- Newton's method and fixed-point iterations.
- Direct methods for solving linear equations, Gaussian elimination and LU-decomposition.
- Eigenvalues and eigenvectors, numerical calculation.
- Iterative methods for solving linear equations.
- Interpolation by polynomials and splines.
- Least squares approximation.
- Numerical differentiation and integration.
- Extrapolation in the calculation of integrals. Gaussian integration formulas.
- One-step methods for solving initial value problems for ordinary differential equations.
- Multistep methods.
- Ordinary differential equations of higher order.
- Systems of differential equations.