1. Introduction to numerical mathematics: basic properties of matrices, errors, conditioning of problems and algorithms.
2.Direct methods for solving systems of linear equations: Gaussian elimination, pivoting, LU decomposition, Cholesky decomposition.
3. Iterative methods for solving systems of linear equations: Jacobi and Gauss–Seidel methods, conjugate gradient method.
4. Interpolation: direct computation of the interpolation polynomial, Lagrange and Newton interpolation polynomials, splines.
5. Numerical differentiation: basic formulas. Numerical integration: Newton–Cotes formulas, Gaussian quadrature formulas.
6. Solution of nonlinear equations: bisection method, Newton’s method, fixed-point method.
7. Systems of nonlinear equations: Newton’s method and its modifications, fixed-point method.
8. Solution of ordinary differential equations: Euler’s method, Runge–Kutta methods.
9. Eigenvalues and eigenvectors: power method, LR decomposition method, spectral decomposition.
10. Descriptive statistics: numerical and graphical processing of quantitative data.
11. Inferential statistics: confidence intervals for estimating an unknown parameter, hypothesis testing for a parameter.
12. Nonparametric hypothesis testing: tests of data normality.
13. Simple linear regression analysis: least squares method, tests of regression coefficients, test of the overall adequacy of the regression model, coefficient of determination.
2.Direct methods for solving systems of linear equations: Gaussian elimination, pivoting, LU decomposition, Cholesky decomposition.
3. Iterative methods for solving systems of linear equations: Jacobi and Gauss–Seidel methods, conjugate gradient method.
4. Interpolation: direct computation of the interpolation polynomial, Lagrange and Newton interpolation polynomials, splines.
5. Numerical differentiation: basic formulas. Numerical integration: Newton–Cotes formulas, Gaussian quadrature formulas.
6. Solution of nonlinear equations: bisection method, Newton’s method, fixed-point method.
7. Systems of nonlinear equations: Newton’s method and its modifications, fixed-point method.
8. Solution of ordinary differential equations: Euler’s method, Runge–Kutta methods.
9. Eigenvalues and eigenvectors: power method, LR decomposition method, spectral decomposition.
10. Descriptive statistics: numerical and graphical processing of quantitative data.
11. Inferential statistics: confidence intervals for estimating an unknown parameter, hypothesis testing for a parameter.
12. Nonparametric hypothesis testing: tests of data normality.
13. Simple linear regression analysis: least squares method, tests of regression coefficients, test of the overall adequacy of the regression model, coefficient of determination.