Course details

# Numerical Methods and Probability

INM Acad. year 2019/2020 Winter semester 5 credits

Guarantor

Deputy Guarantor

Language of instruction

Completion

Time span

Assessment points

Department

Lecturer

Instructor

Subject specific learning outcomes and competences

Learning objectives

Prerequisites

- Mathematical Analysis (IMA)

Prerequisite kwnowledge and skills

Study literature

Fundamental literature

- Ralston, A.: Základy numerické matematiky. Praha, Academia, 1978 (in Czech).
- Horová, I.: Numerické metody. Skriptum PřF MU Brno, 1999 (in Czech).
- Maroš, B., Marošová, M.: Základy numerické matematiky. Skriptum FSI VUT Brno, 1997 (in Czech).
- Loftus, J., Loftus, E.: Essence of Statistics. Second Edition, Alfred A. Knopf, New York 1988.
- Taha, H.A.: Operations Research. An Introduction. Fourth Edition, Macmillan Publishing Company, New York 1989.
- Montgomery, D.C., Runger, G.C.: Applied Statistics and Probability for Engineers. Third Edition. John Wiley & Sons, Inc., New York 2003

Syllabus of lectures

- Introduction to numerical methods.
- Numerical solution of linear systems.
- Numerical solution of non-linear equations and systems.
- Approximation, interpolation.
- Numercial integration and differentiation.
- ODE's: Introduction, numerical solution of first-order initial value problems.
- Introduction to statistics, vizualization of statistical data.
- Introduction to probability theory, probability models, conditional and complete probability.
- Discrete and continuous random variables.
- Selected discrete distributions of probability.
- Selected continuous distributions of probability.
- Statistical testing.
- Reserve, revision, consultations.

Syllabus of numerical exercises

- Classical and geometric probabilities.
- Discrete and continuous random variables.
- Expected value and dispersion.
- Binomial distribution.
- Poisson and exponential distributions.
- Uniform and normal distributions, z-test.
- Mean value test, power.

Syllabus of computer exercises

- Nonlinear equation: Bisection method, regula falsi, iteration, Newton method.
- System of nonlinear equtations, interpolation.
- Splines, least squares method.
- Numerical differentiation and integration.
- Ordinary differential equations, analytical solution.
- Ordinary differential equations, analytical solution.

Progress assessment

- Five 6-point written tests: 30 points,
- final exam: 70 points.

Passing boundary for ECTS assessment: 50 points.

Controlled instruction

Exam prerequisites

Schedule

Day | Type | Weeks | Room | Start | End | Lect.grp | Groups | Info |
---|---|---|---|---|---|---|---|---|

Mon | comp.lab | lectures | T8/522 | 07:00 | 08:50 | 2BIA 3BIT | xx | Novák |

Mon | lecture | lectures | T12/2.173 | 09:00 | 10:50 | 2BIA 3BIT | xx | Novák |

Mon | comp.lab | lectures | T8/522 | 09:00 | 10:50 | 2BIB 3BIT | xx | Fusek |

Mon | lecture | lectures | T10/1.36 | 11:00 | 12:50 | 2BIB 3BIT | xx | Fuchs |

Mon | comp.lab | lectures | T8/522 | 11:00 | 12:50 | 2BIA 3BIT | xx | Novák |

Mon | comp.lab | lectures | T8/522 | 13:00 | 14:50 | 2BIB 3BIT | xx | Fusek |

Mon | comp.lab | lectures | T8/522 | 15:00 | 16:50 | 2BIA 3BIT | xx | Fuchs |

Mon | comp.lab | lectures | T8/522 | 17:00 | 18:50 | 2BIB 3BIT | xx | Fuchs |

Wed | comp.lab | lectures | T8/322 | 15:00 | 16:50 | 2BIB 3BIT | xx | Fuchs |

Thu | comp.lab | lectures | T8/522 | 07:00 | 08:50 | 2BIA 3BIT | xx | Fusek |

Thu | comp.lab | lectures | T8/522 | 09:00 | 10:50 | 2BIA 3BIT | xx | Fusek |

Thu | comp.lab | lectures | T8/522 | 15:00 | 16:50 | 2BIB 3BIT | xx | Fuchs |

Thu | comp.lab | lectures | T8/522 | 17:00 | 18:50 | 2BIA 3BIT | xx | Fuchs |

Course inclusion in study plans