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 pointsB (very good)
35-39 pointsC (good)
30-34 pointsD (satisfactory)
25-29 pointsE (sufficient)
0-24 pointsF (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