Course detail
Mathematics 3
FEKT-BMA3Acad. year: 2012/2013
Numerical mathematics: numerical errors, functional approximation, interpolation and splines, least squares method, numerical derivation and integration, numerical solving of differential equations.
Probability: events and probabilities, conditional probability, independent events, the Bayes theorem, random variable, probability distributions (chosen types), standard normal distribution.
Mathematical statistics: statistical measures, tests.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course curriculum
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
Hlavičková, I., Hliněná, D.: Matematika 3 - sbírka úloh z pravděpodobnosti. Elektronický text FEKT VUT, Brno, 2010 (CS)
Novák, M.: Matematika 3 - sbírka příkladů z numerických metod. Elektronický text FEKT VUT, Brno, 2010 (CS)
Recommended reading
Zapletal, J. Základy počtu pravděpodobnosti a matematické statistiky. Skriptum FEI VUT. Brno: PC-DIR, 1995. (CS)
Classification of course in study plans
- Programme EECC Bc. Bachelor's
branch B-AMT , 2 year of study, winter semester, compulsory
branch B-MET , 2 year of study, winter semester, compulsory
branch B-TLI , 2 year of study, winter semester, compulsory
branch B-SEE , 2 year of study, winter semester, compulsory
branch B-EST , 2 year of study, winter semester, compulsory - Programme EEKR-CZV lifelong learning
branch EE-FLE , 1 year of study, winter semester, compulsory
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2. Interpolation, least squares method.
3. Spline, numerical methods of differentiation.
4. Numerical integration - trapezium and Simpson methods.
5. Solving ODE - Euler method and modifications of the method. Runge - Kutta method.
6. Solving ODE - Euler method for a system of equations, shooting method, finite difference method. Multistep methods.
7. Probabilistic models (classical and geometrical probabilities, discrete and continuous random variables).
8. Expected value and dispersion.
9. Binomial distribution. Fundamentals of statistical tests. The sign test.
10.Poisson and exponential distributions. Their application in queueing theory.
11.Normal distribution. Central limit theorem. Approximation of binomial distribution by means of normal distribution. Z-test and power.
12.The mean expected value test.
Exercise in computer lab
Teacher / Lecturer
Syllabus
2. Iterative metod, Newton method.
3. Systems of nonlinear equations, interpolation.
4. Spline, least squares method.
5. Numerical differentiation and integration.
6. Numerical methods for ordinary differential equations - Euler method, Runge - Kutta method, finite difference method.
7. Classical and geometrical probability.
8. Discrete and continuous random variable.
9. Expected value and dispersion.
10. Binomial distribution. The sign test.
11. The Poisson and exponential distributions, queuing theory.
12. Uniform and normal distributions, binomial approximation of normal distribution, z-test.
(13. Mean expected value test, power.)