Course details

# Numerical Methods and Probability

INM Acad. year 2010/2011 Winter semester 5 credits

Guarantor

Language of instruction

Completion

Time span

Assessment points

Department

Subject specific learning outcomes and competences

Learning objectives

Prerequisites

- Mathematical Analysis (IMA)

Prerequisite kwnowledge and skills

Study literature

- Chapra, S.C., Canale, R.P.: Numerical Methods for Engineers. Fourth Edition. McGraw-Hill 2002, New York (the sample book can be borrowed from the teacher).
- Loftus, J., Loftus, E.: Essence of Statistics. Second Edition, Alfred A. Knopf, New York 1988 (the book can be borrowed from the technical library Brno, Kounicova Street).

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

- Banach theorem. Iterative methods for linear systems of equations.
- Interpolation, splines.
- Least squares method, numerical differentiation.
- Numerical integration: trapezoid and Simpson rules.
- Ordinary differential equations, analytical solution.
- Ordinary differential equations, numerical solution.
- Test 1 (15 points).
- Probability models: classical and geometric probabilities, discrere and continuous random variables.
- Expected value and dispersion.
- Poisson and exponential distributions.
- Uniform and normal distributions. Central limit theorem, z-test, power.
- Mean value test.
- Test 2 (15), review.

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

- Three 5-point homeworks: 15 points,
- five 3-point written tests: 15 points,
- final exam: 70 points.

Passing bounary for ECTS assessment: 50 points.

Controlled instruction

Exam prerequisites

Course inclusion in study plans