KMA/NM1M Numerical Methods 1

Lecturer: Jitka Machalová
Lecture: 2 hours/week + exercise 2 hours/week
Credits: 4
Winter semester
Form of course completion: course credit, exam

• Introduction to numerice methods, error analysis, condition numbers.
• Forward, backward and dividend differences  their properties and computing.
• Difference equations and their solution.
• Introduction to interpolation – statement of the problem, existence and uniqueness of solution.
• Lagrange interpolation, Newton interpolation and interpolation using function values only.
• Error in polynomial interpolation. Chebyschev orthogonal polynomials and thein using in interpolation.
• Iterative linear interpolation. Hermite interpolation.
• Least squares approximation of functions and least squares approximation over discrete sets of points.
• Numerical differentiation – formulas and error estimation.
• Numerical integration – basic rules and notions.
• Gaussian quadrature formulae.
• Newton-Cotes quadrature formulae. Composite quadrature formulae.