MU:MU10136 Numerical Methods - Course Information
MU10136 Numerical Methods
Mathematical Institute in OpavaSummer 2019
- Extent and Intensity
- 2/0/0. 4 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- RNDr. Petra Nábělková, Ph.D. (lecturer)
- Guaranteed by
- RNDr. Petra Nábělková, Ph.D.
Mathematical Institute in Opava - Prerequisites (in Czech)
- MU10130 Mathematical Analysis II && MU10936 Numerical Methods - Exercises
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Applied Mathematics in Risk Management (programme MU, B1101)
- Computer Science and Technology (programme FPF, B1801 Inf)
- Mathematical Methods in Economics (programme MU, B1101)
- Course objectives (in Czech)
- Cílem výuky tohoto předmětu je seznámit studenty se základními numerickými přístupy k řešení problémů, se kterými se již dříve setkali v matematické analýze a algebře.
- Syllabus
- 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.
- 1. Numerical representation (representation of numbers, origin and classification of errors, absolute and relative error, cumulative error, errors of arithmetic operations).
- Literature
- recommended literature
- I. Horová. Numerické metody. Masarykova univerzita v Brně, Brno, 1999. ISBN 80-210-2202-7. info
- J. Segethová. Základy numerické matematiky. Karolinum, Praha, 1998. ISBN 80-7184-596-5. info
- VITÁSEK, E. Numerické metody. SNTL, Praha, 1987. info
- Z. Riečanová a kol. Numerické metody a matematická štatistika. Alfa, Bratislava, 1987. ISBN 063-559-87. info
- Language of instruction
- Czech
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
- Enrolment Statistics (Summer 2019, recent)
- Permalink: https://is.slu.cz/course/sumu/summer2019/MU10136