Course: Numerical Analysis

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Course title Numerical Analysis
Course code MU/03033
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • HASÍK Karel, doc. RNDr. Ph.D.
  • MÁLEK Michal, doc. RNDr. Ph.D.
Course content
1. Numerical representation (representation of numbers, origin and classification of errors, absolute and relative error, cumulative error, errors of arithmetic operations). 2. Approximation (choosing the class of approximating functions, least squares method). 3. Interpolation (estimating interpolation error, iterated interpolation, Lagrange, Hermite and Newton polynomials, interpolation on equidistant nodes, Fraser diagram, inverse interpolation, splines). 4. Numerical solution of nonlinear equations (simple iteration method, bisection method, tangent method, secant methods, regula falsi). 5. Numerical solution of systems of equations (Gauss elimination with control column, LU-decomposition, Jacobi, Gauss-Seidl and Newton-Raphson methods, convergence of methods). 6. Sturm sequence (localization of real roots of a polynomial, Sturm sequence). 7. Numerical integration (numerical quadratire of definite integrals, rectangle, trapezoid and Simpson methods, error estimates). 8. Numerical methods for differential equations (solving initial value problems for ordinary differential equations, power series solutions, Picard approcimations, Euler polygon, Runge-Kutta methods, order of a method). 9. Mesh method for solution of boundary value problems for partial differential equations.

Learning activities and teaching methods
unspecified
Recommended literature
  • A. Ralston. Základy numerické matematiky. Praha, 1978.
  • E. Vitásek. Numerické metody. SNTL, Praha, 1987.
  • I. Horová. Numerické metody. Masarykova univerzita v Brně, Brno, 1999. ISBN 80-210-2202-7.
  • J. Segethová. Základy numerické matematiky. Karolinum, Praha, 1998. ISBN 80-7184-596-5.
  • Z. Riečanová a kol. Numerické metody a matematická štatistika. Alfa, Bratislava, 1987. ISBN 063-559-87.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Mathematics (2014-IVT) Mathematics courses 3 Summer
Mathematical Institute in Opava Applied Mathematics (2) Mathematics courses 1 Summer
Mathematical Institute in Opava Mathematics (2014-F) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematics (2-F) Mathematics courses 3 Summer
Mathematical Institute in Opava Applied Mathematics (1) Mathematics courses 1 Summer
Mathematical Institute in Opava Mathematics (1-IVT) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematical Analysis (1-IVT) Mathematics courses 4 Summer
Mathematical Institute in Opava Mathematical Analysis (1) Mathematics courses 1 Summer