Course details

# Numerical Methods and Probability

INM Acad. year 2017/2018 Winter semester 5 credits

Guarantor

Language of instruction

Completion

Time span

Assessment points

Department

Lecturer

Instructor

Novák Michal, doc. RNDr., Ph.D. (DMAT FEEC BUT)

Svoboda Zdeněk, RNDr., CSc. (DMAT FEEC BUT)

Subject specific learning outcomes and competences

Learning objectives

Prerequisites

- Mathematical Analysis (IMA)

Prerequisite kwnowledge and skills

Study literature

- Fajmon, B., Hlavičková, I., Novák, M., Vítovec, J.: Numerical Methods and Probability (Information technology), VUT v Brně, 2014
- Hlavičková, I., Hliněná, D.: Matematika 3. Sbírka úloh z pravděpodobnosti. VUT v Brně, 2015 (in Czech)
- Hlavičková, I., Novák, M.: Matematika 3 (zkrácená celoobrazovková verze učebního textu). VUT v Brně , 2014 (in Czech)
- Novák, M.: Matematika 3 (komentovaná zkoušková zadání pro kombinovanou formu studia). VUT v Brně, 2014 (in Czech)
- Novák, M.: Mathematics 3 (Numerical methods: Exercise Book), 2014

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.

Progress assessment

- Ten 3-point written tests: 30 points,
- final exam: 70 points.

Passing bounary for ECTS assessment: 50 points.

Controlled instruction

Exam prerequisites

Course inclusion in study plans