Course detail
Mathematics III-B
FSI-CM-KAcad. year: 2010/2011
The course is intended as an introduction to basic methods applied for solving of ordinary differential equations and problems of mathematical statistics.
The knowledge of the basic theory of differential equations and methods of solving is an important foundation for further study of physical and technical disciplines, especially those connected with mechanics.
Statistical methods are concentrated on descriptive statistics, random events, probability, random variables and vectors, random sample, parameters estimation and tests of hypotheses. The practicals cover problems and applications in mechanical engineering.
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
Examination (written form): practical part (2 examples from ordinary differential equations; 2 examples from mathematical statistics) with own summary of formulas; theoretical part (4 questions concerning basic terms, their properties, sense and practical use); evaluation: student may achieve 0-20 point for each example and 0-5 point for each theoretical question; classification according to the total sum of points achieved: excellent (90 - 100 points), very good (80 - 89 points), good (70 - 79 points), satisfactory (60 - 69 points), sufficient (50 - 59 points), failed (0 - 49 points).
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
Montgomery, D. C. - Renger, G.: Probability and Statistics. New York : John Wiley & Sons, Inc.,1996.
Sprinthall, R. C.: Basic Statistical Analysis. Boston : Allyn and Bacon, 1997.
Recommended reading
Karpíšek, Z.: Matematika IV - Statistika a pravděpodobnost. 2. vydání. Brno : FSI VUT v Akademickém nakladatelství CERM Brno, 2003.
Karpíšek, Z. – Popela, P. – Bednář, J.: Statistika a pravděpodobnost. Učební pomůcka - studijní opora pro kombinované studium. Brno : FSI VUT v Akademickém nakladatelství CERM Brno, 2002.
Classification of course in study plans
Type of course unit
Guided consultation
Teacher / Lecturer
Syllabus
2. Analytical methods of solving of 1st order ODE.
3. Higher order ODEs. Properties of solutions and methods of solving of higher order homogeneous linear ODEs.
4. Properties of solutions and methods of solving of higher order non-homogeneous linear ODEs.
5. Systems of 1st order ODEs. Properties of solutions and methods of solving of homogeneous linear systems of 1st order ODEs.
6. Properties of solutions and methods of solving of non-homogeneous linear systems of 1st order ODEs.
7. Boundary value problem for 2nd order ODEs.
8. Descriptive statistics.
9. Random events and probability.
10. Random variable and vector, functional and numerical characteristics.
11. Basic probability distributions (Bi, H, Po, N), properties and use.
12. Random sample, parameter estimations (Bi, N).
13. Testing statistical hypotheses of parameters (Bi, N).