Title:

Numerical Methods and Probability

Code:INM
Ac.Year:2018/2019
Sem:Winter
Curriculums:
ProgrammeFieldYearDuty
IT-BC-3BIT2ndCompulsory
Language of Instruction:Czech
Credits:5
Completion:credit+exam (written)
Type of
instruction:
Hour/semLecturesSeminar
Exercises
Laboratory
Exercises
Computer
Exercises
Other
Hours:2600260
 ExamsTestsExercisesLaboratoriesOther
Points:7030000
Guarantor:Novák Michal, RNDr., Ph.D. (DMAT)
Deputy guarantor:Fuchs Petr, RNDr., Ph.D. (DMAT)
Lecturer:Fuchs Petr, RNDr., Ph.D. (DMAT)
Novák Michal, RNDr., Ph.D. (DMAT)
Instructor:Fuchs Petr, RNDr., Ph.D. (DMAT)
Novák Michal, RNDr., Ph.D. (DMAT)
Svoboda Zdeněk, RNDr., CSc. (DMAT)
Faculty:Faculty of Electrical Engineering and Communication BUT
Department:Department of Mathematics FEEC BUT
Prerequisites: 
Discrete Mathematics (IDA), DMAT
Mathematical Analysis (IMA), DMAT
Schedule:
DayLessonWeekRoomStartEndLect.Gr.St.G.EndG.
Moncomp.lab - NováklecturesT8/52207:0008:502BIA1010
Moncomp.lab - NováklecturesT8/52207:0008:503BITxxxx
Monlecture - NováklecturesT12/2.17309:0010:502BIA
Monlecture - NováklecturesT12/2.17309:0010:503BITxxxx
Monlecture - FuchslecturesT10/1.3611:0012:502BIB
Monlecture - FuchslecturesT10/1.3611:0012:503BITxxxx
Monexam - 2. oprava2019-01-28T8/01012:0013:502BIA
Monexam - 2. oprava2019-01-28T8/01012:0013:502BIB
Monexam - 2. oprava2019-01-28T8/01012:0013:503BIT
Moncomp.lab - NováklecturesT8/52213:0014:502BIA1111
Moncomp.lab - NováklecturesT8/52213:0014:503BITxxxx
Moncomp.lab - FuchslecturesT8/50315:0016:502BIB2020
Moncomp.lab - FuchslecturesT8/50315:0016:503BITxxxx
Moncomp.lab - FuchslecturesT8/50317:0018:502BIB2121
Moncomp.lab - FuchslecturesT8/50317:0018:503BITxxxx
Thucomp.lab - NováklecturesT8/52207:0008:502BIA1212
Thucomp.lab - NováklecturesT8/52207:0008:503BITxxxx
Thucomp.lab - NováklecturesT8/52209:0010:502BIA1313
Thucomp.lab - NováklecturesT8/52209:0010:503BITxxxx
Thuexam - 1. oprava2019-01-17T8/01009:0010:502BIA
Thuexam - 1. oprava2019-01-17T8/01009:0010:502BIB
Thuexam - 1. oprava2019-01-17T8/01009:0010:503BIT
Thucomp.lab - NováklecturesT8/52211:0012:502BIA1414
Thucomp.lab - NováklecturesT8/52211:0012:503BITxxxx
Thucomp.lab - FuchslecturesT8/52213:0014:502BIB2222
Thucomp.lab - FuchslecturesT8/52213:0014:503BITxxxx
Thucomp.lab - FuchslecturesT8/52215:0016:502BIB2323
Thucomp.lab - FuchslecturesT8/52215:0016:503BITxxxx
Thucomp.lab - FuchslecturesT8/52217:0018:502BIB2424
Thucomp.lab - FuchslecturesT8/52217:0018:503BITxxxx
Friexam - řádná2019-01-11T12/2.17311:0012:502BIA
Friexam - řádná2019-01-11T12/2.17311:0012:502BIB
Friexam - řádná2019-01-11T12/2.17311:0012:503BIT
Friexam - řádná2019-01-11D10511:0012:502BIA
Friexam - řádná2019-01-11D10511:0012:502BIB
Friexam - řádná2019-01-11D10511:0012:503BIT
Friexam - řádná2019-01-11D020611:0012:502BIA
Friexam - řádná2019-01-11D020611:0012:502BIB
Friexam - řádná2019-01-11D020611:0012:503BIT
Friexam - řádná2019-01-11D020711:0012:502BIA
Friexam - řádná2019-01-11D020711:0012:502BIB
Friexam - řádná2019-01-11D020711:0012:503BIT
 
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.
Description:
  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.
Knowledge and skills required for the course:
  Secondary school mathematics and some topics from Discrete Mathematics and Mathematical Analysis courses.
Learning outcomes and competencies:
  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.
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.
Fundamental literature:
 
  1. Ralston, A.: Základy numerické matematiky. Praha, Academia, 1978 (in Czech).
  2. Horová, I.: Numerické metody. Skriptum PřF MU Brno, 1999 (in Czech).
  3. Maroš, B., Marošová, M.: Základy numerické matematiky. Skriptum FSI VUT Brno, 1997 (in Czech).
  4. Loftus, J., Loftus, E.: Essence of Statistics. Second Edition, Alfred A. Knopf, New York 1988.
  5. Taha, H.A.: Operations Research. An Introduction. Fourth Edition, Macmillan Publishing Company, New York 1989.
  6. Montgomery, D.C., Runger, G.C.: Applied Statistics and Probability for Engineers. Third Edition. John Wiley & Sons, Inc., New York 2003
Study literature:
 
  • 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
Controlled instruction:
  Ten written tests.
Progress assessment:
  
  • 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.
 

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