Studijní plán:

Sylabus

• Taylor expansion, polynomial substitution, approximation of irrational numbers, evaluation of polynomials, Horner scheme.
• Numerical solution of nonlinear problems (bisection m., regula falsi m., tangent and secant m.), numerical optimization (Nelder-Mead method).
• Direct methods of numerical solution of systems of linear equations, conditioning and stability, vector and matrix norms.
• Iterative methods for solution of systems of linear equations.
• Interpolation polynomials, Lagrange and Newton methods.
• Least squares approximations.
• Numerical quadrature, rectangle, trapezoidal and Simpson rules.
• Orthogonal polynomials, Gauss quadrature.
• Numerical derivative.
• Numerical solution of differential equations, initial and boundary problems. Euler method. Finite difference method.

Doporučená literatura

• Jeffrey R. Chasnov, Introduction to Numerical Methods, Lecture notes for MATH 3311 (http://www.math.ust.hk/~machas/numerical-methods.pdf)
  
• Kendall E. Atkinson, An Introduction to Numerical Analysis, John Wiley & Sons 1988, (http://math.science.cmu.ac.th/docs/qNA2556/ref_na/Katkinson.pdf)
  
• Douglas N. Arnold, A Concise Introduction to Numerical Analysis (http://www.ima.umn.edu/~arnold/597.00-01/nabook.pdf)
  

Anotace

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