714-0781/04 – Numerical methods and statistics (NMS)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 4 |
| Subject guarantor | prof. RNDr. Radek Kučera, Ph.D. | Subject version guarantor | prof. RNDr. Radek Kučera, Ph.D. |
| Study level | undergraduate or graduate | | |
| | Study language | English |
| Year of introduction | 2019/2020 | Year of cancellation | 2019/2020 |
| Intended for the faculties | FMT | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
The aim of this course is to acquaint students with the numerical solution of mathematical problems and with the basic methods of analysing statistical data. The main accent lays in explanations of fundamental principles of methods so that the students should know to choose appropriate methods for problems arising in the other courses of the study or in the technical practice. An important ingredient of the course consists in the algorithmic implementation of methods and in the utilization of existing computer programms for numerical computations and statistical analyses.
The graduate of this course should know:
• to recognize problems suitable for solving by numerical procedures and to find an appropriate numerical method;
• to decide whether the computed solution is sufficiently accurate and, in case of need, to assess reasons of inaccuracies;
• to propose an algorithmic procedure for solving the problem and to choice a suitable computer environment for its realization.
Teaching methods
Lectures
Individual consultations
Tutorials
Other activities
Summary
The course is devoted to basic numerical methods of the linear algebra and mathematical analysis and to basic methods of analysing statistical data. The following themes will be presented: iterative methods for solving of nonlinear equations, direct and iterative methods for solving of linear systems, eigenvalue problems, interpolation and approximation of functions, numerical computation of derivatives and integrals, solving of ordinary differential equations, estimations of statistical parameters and
testing of hypotheses. The programming system Matlab is used during the course.
Compulsory literature:
1. Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007.
Recommended literature:
1. Süli, E., Mayers, D.: An introduction to Numerical Analysis. Cambridge University Press, 2003.
2. Van Loan, C. F.: Introduction to scientific computing. Prentice Hall, Upper
Saddle River, NJ 07459, 1999.
Way of continuous check of knowledge in the course of semester
Tests and credits.
Exercises: conditions for obtaining credit points (CP
- participation in exercises, 20% can be to apologize,
- completion of three written tests, 0-15 CP,
- completion of two programs, 5 CP.
Exam:
- written exam 0-60 CP, successful completion at least 25 CP,
- oral exam 0-20 CP, successful completion at least 5 CP.
E-learning
Other requirements
They are no other requirements for students.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1st Course contents, the issue of errors, stability of calculations.
2nd Solution of nonlinear equations, separation of roots, the simplest methods.
3rd Newton's method and fixed-point iterations.
4th Direct methods for solving linear equations, Gaussian elimination and LU-decomposition.
5th Eigenvalues and eigenvectors, numerical calculation.
6th Iterative methods for solving linear equations.
7th Interpolation by polynomials and splines.
8th Least squares approximation.
9th Numerical differentiation and integration.
10th Extrapolation in the calculation of integrals. Gaussian integration formulas.
11th One-step methods for solving initial value problems for ordinary differential equations.
12th Multi-step methods.
13th Statistical data processing, empirical characteristics.
14th Parameter estimation and testing of hypotheses.
Conditions for subject completion
Conditions for completion are defined only for particular subject version and form of study
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.