Mathematics 2

Kód předmětu: 101MT02
Garant předmětu: Mgr. Yuliya Namlyeyeva, Ph.D.
Zakončení předmětu: Z,ZK
Počet kreditů: 6 kred.
Rozsah výuky: 2+3
Web předmětu: https://mat.fsv.cvut.cz/vyuka/bakalari/eng/ls/MT02/

Anotace(semestr B232)
https://mat.fsv.cvut.cz/vyuka/bakalari/eng/ls/MT02/
Obsah 
Integral calculus

Primitive functions, indefinite integral, “tabular integrals”, methods of integration by parts (per partes) and substitutions for indefinite integrals. Integration of rational functions (with simple imaginary roots in denominators at most, real roots of arbitrary multiplicity). Select special substitutions.
Definite integral, Newton-Leibniz''s formula, per partes and substitutions for definite integrals, comparing of integrals without their computation. Improper integrals, convergence and divergence, calculation.
Applications to integral calculus: area of plane figures (plane sheets), volume of solids of revolution, length of graphs of functions, static moments and coordinates of the center of gravity of plane figures.

Functions of more variables

Domains of definition. For functions of two variables level curves and graphs. Partial derivatives of the 1st order and their geometric meaning. Partial derivatives of higher orders. Directional derivatives and their geometric meaning. Gradient. Total differential and its applications.
Implicit functions, existence, derivatives of implicit functions of one variable, partial derivatives of implicit functions of two variables. Equations of tangent lines and normal lines of plane curves, equations of tangent planes and normal lines of surfaces. Extremes, local, constrained, global.

Differential equations

Identification of differential equations of the 1st order, general solutions, particular solutions with initial conditions (Cauchy problems). Separable differential equations (including Cauchy problems). Homogeneous differential equations of the 1st order (including Cauchy problems). Linear differential equations of the 1st order (including Cauchy problems). Exact differential equations (including Cauchy problems).
Literatura 
[1]  https://mat.fsv.cvut.cz/vyuka/bakalari/eng/ls/MT02/references
Návaznosti 
Tento předmět lze klasifikovat až po klasifikaci předmětu 101MT01
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Bez absolvování tohoto předmětu nelze klasifikovat předmět 101MT03
Bez absolvování tohoto předmětu nelze klasifikovat předmět 132TELA
Studijní plány 
Předmět je zařazen do následujících studijních plánů:

- studijní plán Civil Engineering (BD2020), skupina Civil Engineering, 2nd semester (BD20200200), dop. semestr 2 (valid from 2020/21 to 2022/23 )
- studijní plán Civil Engineering (BD2023), skupina Civil Engineering, 2nd semester (BD20200200), dop. semestr 2 (valid from 2023/24 )