Numerical Methods and Probability

• 26 hrs lectures
• 26 hrs exercises

• 70 pts final exam (written part)
• 30 pts mid-term test (written part)

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

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.

Secondary school mathematics and some topics from Discrete Mathematics and Mathematical Analysis courses.

• 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
• 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

1. Introduction to numerical methods.
2. Numerical solution of linear systems.
3. Numerical solution of non-linear equations and systems.
4. Approximation, interpolation.
5. Numercial integration and differentiation.
6. ODE's: Introduction, numerical solution of first-order initial value problems.
7. Introduction to statistics, vizualization of statistical data.
8. Introduction to probability theory, probability models, conditional and complete probability.
9. Discrete and continuous random variables.
10. Selected discrete distributions of probability.
11. Selected continuous distributions of probability.
12. Statistical testing.
13. Reserve, revision, consultations.

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

• Ten 3-point written tests: 30 points,
• final exam: 70 points.
  Passing bounary for ECTS assessment: 50 points.
• 
  Exam prerequisites:
  To pass written tests with at least 10 points.

Ten written tests.

To pass written tests with at least 10 points.