### Mathematics 3

Syllabus (Mathematics):
1. Linear diferential equations of the n-th order, the initial value problem. Homogeneous equations with constant coefficients. Reductions of the order.
2. Nonhomogeneous equations, variations of parameters, the method of undetermined coefficients for special quasi-polynomial right-hand side.
3. 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.
4. 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.
5. Double and triple Riemann integral, Fubini theorem, substitution (polar, spherical and cylindrical coordinates), applications of double and triple integral.
6. Line integral of a function and its applications.
7. Line integral of a vector field and its applications, independence on the path, Green’s theorem.

Syllabus (Statistics):
1. Introduction; Descriptive statistics for one sample. Boxplot, outliers.
2. Descriptive statistics for two samples. Introduction to linear regression.
3. Introduction to probability theory. Classical probability assessment.
4. Conditional probability; independence of events.
5. Discrete random variables; expected value and variance.
6. Binomial distribution with applications.
7. Continuous random variables; expected value and variance.
8. Normal probability distribution with applications.
9. 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.

References (Mathematics):

F. Bubeník: Mathematics for Engineers, Prague 2007

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

References (Statistics):

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