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Course detail
Mathematics IIIB
Course unit code:  FSICMK  

Academic year:  2016/2017  
Type of course unit:  compulsory  
Level of course unit:  Bachelor's (1st cycle)  
Year of study:  2  
Semester:  winter  
Number of ECTS credits:  4  



























Type of course unit:
Tuition:  13 hours, optionally 

Teacher / Lecturer:  Ing. Josef Bednář, Ph.D. 
Syllabus:  1. ODE. Basic terms. Existence and uniqueness of solutions. 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 nonhomogeneous 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 nonhomogeneous 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). 
Controlled Selfstudy:  26 hours, compulsory 
Teacher / Lecturer:  doc. RNDr. Jan Čermák, CSc. 
Syllabus:  1. Calculation of integrals  revision. 2. Analytical methods of solving of 1st order ODEs. 3. Analytical methods of solving of 1st order ODEs (continuation). 4. Higher order linear homogeneous ODEs. 5. Higher order nonhomogeneous linear ODEs. 6. Systems of 1st order linear homogeneous ODEs. 7. Systems of 1st order linear nonhomogeneous ODEs. 8. Descriptive statistics (univariate and bivariate sample). 9. Probability, conditioned probability, independent events. 10. Functional and numerical characteristics of random variable. 11. Probability distributions (Bi, H, Po, N). 12. Point and interval estimates of parameters N and Bi. 13. Testing hypotheses of parameters N and Bi. 