714-0253/01 – Numerical Methods (NM)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 4 |
| Subject guarantor | RNDr. Jana Staňková, Ph.D. | Subject version guarantor | RNDr. Jana Staňková, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Optional |
| Year | 1 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2015/2016 | Year of cancellation | 2019/2020 |
| Intended for the faculties | FAST | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
The first part of this course is dedicated to finding numerical solutions of
mathematical problems. These problems can arise from other courses as
well as from practice. The main emphasis lays in
explanation of fundamental principles of numerical methods and of their
general properties. The students learn how to decide which numerical
procedure is a suitable tool for solving a specific problem. An
important ingredient of the course is algorithmic implementation of the
learned numerical methods. The students learn how to use existing
software specialized for numerical computations, too.
The graduate of this course should be able:
* to recognize problems solvable by numerical procedures and to find
an appropriate numerical method;
* to decide whether the obtained numerical solution is accurate
enough and, if it is not the case, to assess the reasons of inaccuracies;
* to propose an algorithmic procedure to solving a problem and to
choose a suitable software for its realization;
Teaching methods
Lectures
Tutorials
Summary
The first part of this course deals with selected issues in numerical computations
(including sources and types of numerical errors, conditionality of
certain problems and algorithms), with methods for solving algebraic and
transcendent equations, with solving systems of linear equations, with
interpolation and approximation of functions, with numerical computations
of integrals, and with Cauchy problems for ordinary differential
equations.
Compulsory literature:
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
E-learning
Other requirements
There are no other requirements on students
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
. Problematics of numerical computing . Sources and types of errors. Conditionality of problems and algorithms.
2. Methods for solving algebraic and transcendental equations. The bisection method, the iterative method for solving equations.
3. The Newton method, the Regula-Falsi (False-Position) method, the combined method.
4. Solving systems of linear equations. Direct solution methods. Iterative methods (the Jacobi method, the Seidel method). Matrix norms.
5. Interpolation and approximation of functions. Approximation – the least-square method. Lagrange interpolation polynomials.
6. Newton interpolation polynomials. Spline-function interpolation.
7. Numerical integration. Newton-Cotes quadrature formulas. Composed quadrature formulas. Error estimation.
8. The Richardson extrapolation.
9. Initial value problems for ordinary differential equations. One-step methods. The Euler method. Error estimation using the half-step method.
10. The Runge-Kutta methods. Estimation of the approximation error.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.