Course Details
Mathematics
Academic Year 2025/26
Course Guarantor
Institute
Language of instruction
Czech
Credits
4 credits
Semester
summer
Forms and criteria of assessment
course-unit credit
Offered to foreign students
Not to offer
Course on BUT site
Lecture
13 weeks, 3 hours/week, elective
Syllabus
- 1. Errors in numerical calculations. Numerical methods for one nonlinear equation in one unknown
- 2. Basic principles of iterative methods. The Banach fixed-point theorem.
- 3. Norms of vectors and of matrices, eigenvalues and eigenvectors of matrices. Iterative methods for systems of linear algebraic equations– part I.
- 4. Iterative methods for linear algebraic equations – part II. Iterative methods for systems of nonlinear equations.
- 5. Direct methods for systems of linear algebraic equations, LU-decomposition. Systems of linear algebraic equations with special matrice – part I.
- 6. Systems of linear algebraic equations with special matrices – part II. The methods based on the minimization of a quadratic form.
- 7. Computing inverse matrices and determinants, the stability and the condition number of a matrix.
- 8. Eigenvalues of matrices – the power method. Basic principles of interpolation.
- 9. Polynomial interpolation.
- 10. Interpolation by means of splines. Orthogonal polynoms.
- 11. Approximation by the discrete least squares.
- 12. Numerical differentiation, Richardson´s extrapolation. Numerical integration of functions in one variables – part I.
- 13. Numerical integration of functions in one variables – part II. Numerical integration of functions in two variables.