- Linear diferential equations of the n-th order, the initial value problem. Homogeneous equations with constant coefficients. Reductions of the order.
- Nonhomogeneous equations, variations of parameters, the method of undetermined coefficients for special quasi-polynomial right-hand side.
- Inner product vector spaces, examples. Norm and metric induced by inner product, Cauchy-Schwarz inequality. Boundary value problems for ordinary differential equations. The corresponding eigenvalue problems.
- Symmetric, positive and positive definite linear operators, examples. Eigenvalues and eigenvectors of a linear operator. The solvability of the problem A(u)-l u = f.
- Double and triple Riemann integral, Fubini theorem, substitution (polar, spherical and cylindrical coordinates), applications of double and triple integral.
- Line integral of a function and its applications.
- Line integral of a vector field and its applications, independence on the path, Green’s theorem.

- Introduction; Descriptive statistics for one sample. Boxplot, outliers.
- Descriptive statistics for two samples. Introduction to linear regression.
- Introduction to probability theory. Classical probability assessment.
- Conditional probability; independence of events.
- Discrete random variables; expected value and variance.
- Binomial distribution with applications.
- Continuous random variables; expected value and variance.
- Normal probability distribution with applications.
- Statistical inference.

Seminars are obligatory. During the 5^{th} week the students write the test and during the 10^{th} week a test on computers (both for 40 min.) with
a total amount of points 42 (18+24). 5/42 of these points is tranfserable to exam.

If a student reaches from all tests only 6 points and less the assessment is not awarded.

There is no possibility to repeat the test.

Test Mathematics (90 min.), Statistics (30 min.) with a total amount of points 45 (33 Mathematics, 12 Statistics) (+ at most 5 points transfered from seminars). An additional requirement is to achieve at least 6 points from Statistics.

The results: | > 44 points | A (excellent) |

40-44 points | B (very good) | |

35-39 points | C (good) | |

30-34 points | D (satisfactory) | |

25-29 points | E (sufficient) | |

0-24 points | F (failed) |

No calculators (except of Statistics), mobile phones, cameras or any means of communications are allowed during the test.

In the part Mathematics students can use the textbook F. Bubeník: Mathematics for Engineers. In the part Statistics students can use calculators and any textbook from Statistics.

F. Bubeník: Mathematics for Engineers, Prague 2007

F. Bubeník: Problems to Mathematics for Engineers, Prague 2007

Levine, D. M., Krehbiel, T. C., and Berenson, M. L.: **Business Statistics – A First Course**, Sixth Edition, Pearson International Edition, 2013

De Veaux, R.D., Velleman, P. F., and Bock, D.E.: **Intro Stats**, Third Edition. Pearson International Edition, Addison Wesley, 2009