- 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.
Requirements - Seminars:
Seminars are obligatory. During the 5th week the students write the test and during the 10th 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.
Requirements - Exam:
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