Course details

Probability and Numerical Methods

INM Acad. year 2003/2004 Winter semester 5 credits

Current academic year

Numerical mathematics: Metric spaces, Banach theorem. Solution of nonlinear equations. Approximations of functions, interpolation, least squares method, splines. Numerical derivative and integral. Solution of ordinary differential equations, one-step and multi-step methods. Probability: Random event and operations with events, definition of probability, independent events, total probability. Random variable, characteristics of a random variable. Probability distributions used, law of large numbers, limit theorems.

Details ...

Guarantor

Melkes František, prof. RNDr., CSc.

Language of instruction

Czech

Completion

Examination

Time span

Department

Department of Mathematics (UMAT)

Subject specific learning outcomes and competences

Students apply the gained knowledge in technical subjects when solving projects and writing the Bc. thesis. Numerical methods represent the fundamental element of investigation and practice in the present state of research.

Learning objectives

In the first part the student will be acquainted with some numerical methods (approximation of functions, solution of nonlinear equations, approximate determination of a derivative and an integral, solution of differential equations) which are suitable for modelling various problems of practice. The other part of the subject yields fundamental knowledge from the probability theory (random event, probability, characteristics of random variables, probability distributions) which is necessary for simulation of random processes.

Study literature

  • Fajmon, B., Hlavičková, I., Novák, M., Vítovec, J.: Numerická matematika a pravděpodobnost (Informační technologie), VUT v Brně, 2014
  • Hlavičková, I., Hliněná, D.: Matematika 3. Sbírka úloh z pravděpodobnosti. VUT v Brně, 2015
  • Hlavičková, I., Novák, M.: Matematika 3 (zkrácená celoobrazovková verze učebního textu). VUT v Brně , 2014
  • Novák, M.: Matematika 3 (komentovaná zkoušková zadání pro kombinovanou formu studia). VUT v Brně, 2014
  • Novák, M.: Mathematics 3 (Numerical methods: Exercise Book), 2014

Fundamental literature

  • Ralston, A.: Základy numerické matematiky. Praha, Academia, 1978.
  • Horová, I.: Numerické metody. Skriptum PřF MU Brno, 1999.
  • Maroš, B., Marošová, M.: Základy numerické matematiky. Skriptum FSI VUT Brno, 1997.
  • 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.

Progress assessment

Written mid-term exam.

Course inclusion in study plans

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