CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

# Mathematics 3

Code Completion Credits Range Language
101MT03 Z,ZK 6 3P+2C Czech
Mathematics 2 (101MT02)
Lecturer:
Martin Hála, Yuliya Namlyeyeva
Tutor:
Yuliya Namlyeyeva
Supervisor:
Department of Mathematics
Synopsis:

1.Linear differential equations of the n-th order, initial value problems. Homogeneous equations: fundamental system, general solution. Fundamental system for equation with constant coefficients. Descriptive statistics.

2. Reduction of order. Nonhomogeneous equations: variation of parameters, method of undetermined coefficients. Descriptive statistics: box-plot, outliers. Bivariate data.

3. Dot product of functions in C([a,b]), orthogonality of functions. Setup of a boundary value problem, examples.

Bivariate descriptive statistics. Linear regression.

4. Problem u''+au=f, u(0)=u(pi)=0, eigenvalues and eigenfunctions. Orthogonality of eigenfunctions. Solvability (as it depends on „a“). Some other problems. Introduction to probability theory. Classical probability.

5. Double integral, Fubini Theorem, substitution, polar coordinates. Conditional probability; independent events.

6. Applications of double integral. Discrete random variables.

7. Triple Riemann integral, Fubini Theorem, substitution, cylindrical and spherical coordinates. applications of double and triple integral. Binomial distribution.

8. Applications of triple integral. Continuous random variables.

9.Line integral of a scalar field, applications. Continuous random variable: expected value and variance.

10. Line integral of a vector field, Green Theorem. Normal distribution.

11. Conservative fields. Applications of normal distribution.

12. Applications of line integrals. Inferential statistics.

Requirements:
Syllabus of lectures:
Syllabus of tutorials:
Study Objective:
Study materials:

!F. Bubeník: Mathematics for Engineers. CVUT, 2014, ISBN 978-80-01-03792-8.

!F. Bubeník: Problems to Mathematics for Engineers, CVUT 2014, ISBN 978-80-01-05621-9

?Sherman Stein, Anthony Barcellos, Calculus and Analytic Geometry 5th ed., Mcgraw-Hill 1992, ISBN 978-0070611757

Note:
Time-table for winter semester 2019/2020:
 06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00 roomTH:B-69212:00–13:50(lecture parallel1parallel nr.101)Thákurova 7 (FSv-budova A)B692 roomTH:B-36914:00–16:50(lecture parallel1)Thákurova 7 (FSv-budova A)B369
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-06-04
For updated information see http://bilakniha.cvut.cz/en/predmet2781906.html