Course details

# Probability and Numerical Methods

INM Acad. year 2004/2005 Winter semester 5 credits

Guarantor

Language of instruction

Completion

Time span

Assessment points

Department

Lecturer

Subject specific learning outcomes and competences

Learning objectives

Prerequisites

- Mathematical Analysis (IMA)

Study literature

- Anděl, J.: Statistical Methods. Matfyzpress UK Praha, 1993.
- Diblík, J., Haluzíková, A., Baštinec, J.: Numerical Mathematics and Mathematical Statistics. SNTL Praha, 1987 (university text).
- Horová, I.: Numerical Methods. MU Brno, 1999.
- Nekvinda, M., Šrubař, J., Vild, J.: Introduction to Numerical Mathematics. SNTL Praha 1976.
- Vitásek, E.: Numerical Methods. SNTL Praha, 1987.
- Zapletal, J.: Grounding of Probability Calculus and Mathematical Statistics. PC-DIR Brno, 1995.

Fundamental literature

- Anděl, J.: Statistical methods. Matfyzpress UK Praha, 1993.
- Diblík, J., Haluzíková, A., Baštinec, J.: Numerical Mathematics and Mathematical Statistics. SNTL Praha, 1987 (university text).
- Horová, I.: Numerical Methods. MU Brno, 1999.
- Likeš, J., Machek, J.: Probability Calculus. SNTL Praha, 1987.
- Nekvinda, M., Šrubař, J., Vild, J.: Introduction to Numerical Mathematics. SNTL Praha 1976.
- Ralston, A.: A First Course in Numerical Analysis. Academia Praha, 1978.
- Vitásek, E.: Numerical Methods. SNTL Praha, 1987.
- Zapletal ,J.: Grounding of Probability Calculus and Mathematical Statistics. PC-DIR Brno, 1995.

Syllabus of lectures

- Principle of numerical methods, error classification, accuracy improvement.
- Metric space, completeness, contraction, Banach fixed- point theorem.
- Solving of nonlinear equations.
- Approximation, interpolation polynomial, least squares method, spline.
- Numerical derivative and integral, composite quadrature formulae.
- Solving of ordinary differential equations, one-step methods.
- Multi-step methods.
- Elementary event, operation with events, field of events.
- Definition of probability, conditional probability, event independence, total probability theorem.
- Random variable, distribution function, random variable distribution, probability density.
- Two-dimensional random variable, random variable characteristic.
- Some important distributions, law of large numbers, limit theorems.
- Fundamental concepts, hypothesis testing.

Syllabus of numerical exercises

- Numerical error estimates, Richardson extrapolation.
- Interpolation polynomial.
- Application of Banach theorem.
- Probability.
- Distribution function, probability density.
- Normal distribution.
- Numerical characteristics.

Syllabus - others, projects and individual work of students

- Topic will be given in the beginning of the term. Project must contain theory, solution in the form of a program and conclusion. Valuation: 20 points as a maximum.

Progress assessment

Controlled instruction

Test ... 10 points.

Problems in MATLAB ... 20 points.

Exam prerequisites