Course details

# Numerical Methods and Probability

INM Acad. year 2019/2020 Winter semester 5 credits

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. Rudiments of statistical thinking.

Guarantor

Deputy Guarantor

Fuchs Petr, RNDr., Ph.D. (DMAT FEEC BUT)

Language of instruction

Czech

Completion

Credit+Examination (written)

Time span

26 hrs lectures, 26 hrs pc labs

Assessment points

70 exam, 30 half-term test

Department

Lecturer

Instructor

Subject specific learning outcomes and competences

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.

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.

Prerequisites

Prerequisite kwnowledge and skills

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

Study literature

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

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.

Syllabus of numerical exercises

1. Classical and geometric probabilities.
2. Discrete and continuous random variables.
3. Expected value and dispersion.
4. Binomial distribution.
5. Poisson and exponential distributions.
6. Uniform and normal distributions, z-test.
7. Mean value test, power.

Syllabus of computer exercises

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.

Progress assessment

• Five 6-point written tests: 30 points,
• final exam: 70 points.
Passing boundary for ECTS assessment: 50 points.

Controlled instruction

Five written tests according to the specification of teachers.

Exam prerequisites

To pass written tests with at least 10 points.

Schedule

DayTypeWeeksRoomStartEndLect.grpGroupsInfo
Moncomp.lablectures T8/522 07:0008:50 2BIA 3BIT xx Novák
Monlecturelectures T12/2.173 09:0010:50 2BIA 3BIT xx Novák
Moncomp.lablectures T8/522 09:0010:50 2BIB 3BIT xx Fusek
Monlecturelectures T10/1.36 11:0012:50 2BIB 3BIT xx Fuchs
Moncomp.lablectures T8/522 11:0012:50 2BIA 3BIT xx Novák
Moncomp.lablectures T8/522 13:0014:50 2BIB 3BIT xx Fusek
Moncomp.lablectures T8/522 15:0016:50 2BIA 3BIT xx Fuchs
Moncomp.lablectures T8/522 17:0018:50 2BIB 3BIT xx Fuchs
Wedcomp.lablectures T8/322 15:0016:50 2BIB 3BIT xx Fuchs
Thucomp.lablectures T8/522 07:0008:50 2BIA 3BIT xx Fusek
Thucomp.lablectures T8/522 09:0010:50 2BIA 3BIT xx Fusek
Thucomp.lablectures T8/522 15:0016:50 2BIB 3BIT xx Fuchs
Thucomp.lablectures T8/522 17:0018:50 2BIA 3BIT xx Fuchs

Course inclusion in study plans

• Programme IT-BC-3, field BIT, 2nd year of study, Compulsory