# Mathematics 1

Kód předmětu: 101MT01
Zakončení předmětu: Z,ZK
Počet kreditů: 6 kred.
Rozsah výuky: 2+3
Web předmětu: https://mat.fsv.cvut.cz/bubenik/mat1detail.htm

Anotace (semestr ) 1. Indefinite integral, primitive functions, tabular integrals. Fundamental methods for calculating indefinite integrals: per partes, substitutions. 2. Integration of rational functions (with simple imaginary roots in denominators at most one). 3. Selected special substitutions. 4. Definite integral, fundamental methods for calculating definite integrals: Newton- Leibniz`s formula, per partes, substitutions. 5. Improper integrals, convergence and divergence of improper integrals, methods of computation. 6. Geometrical and physical applications of integral calculus : area of a plane figure, volume of a solid of revolution, length of the graph of a function, static moments and the centre of gravity of a plane figure. 7. Functions of several variables. Definition domains, in case of two variables also level curves and graphs. Partial derivatives, partial derivatives of higher orders. 8. Directional derivatives. Gradient. Total differential. Derivatives and partial derivatives of functions defined implicitly. 9. Equations of tangent and normal lines of a plane curve and tangent planes and normal lines of a surface. 10. Local extrema and local extrema with respect to a set (constrained extrema). 11. Global extrema on a set. 12. Differential equations of the 1st order, separation of variables, homogeneous equations. Cauchy problems. 13. Linear differential equations of the 1st order, variation of a constant. Exact equations. Cauchy problems. 1. Indefinite integral, primitive functions, tabular integrals. Fundamental methods for calculating indefinite integrals: per partes, substitutions. 2. Integration of rational functions (with simple imaginary roots in denominators at most one). 3. Select special substitutions. 4. Definite integral, fundamental methods for calculating definite integrals: Newton-Leibniz''s formula, per partes, substitutions. 5. Improper integrals, convergence and divergence of improper integrals, methods of computation. 6. Geometrical and physical applications of integral calculus: area of a plane figure (plane sheet), volume of a solid of revolution, length of the graph of a function, static moments and the centre of gravity of a plane figure. 7. Domains of definitions, in case of two variables also level curves and graphs. Partial derivatives, partial derivatives of higher orders. 8. Directional derivatives. Gradient. Total differential. Derivatives and partial derivatives of functions defined implicitly. 9. Equations of tangent and normal lines of a plane curve and tangent planes and normal lines of a surface. 10. Local extremes and local extremes with respect to a set (constrained extremes). 11. Global extremes on a set. 12. Differential equations of the 1st order, separation of variables, homogeneous equations. Cauchy problems. 13. Linear differential equations of the 1st order, variation of a constant. Exact equations. Cauchy problems. Povinná literatura:   Bubeník F.: Mathematics for Engineers, Prague, 2014, ISBN 978-80-01-05620-2   Bubeník F.: Problems to Mathematics for Engineers, Prague, 2014, ISBN 978-80-01-05621-9   Rektorys K.: Survey of Applicable Mathematics, Vol. I, II, ISBN 9401583080, 9789401583084 Bez absolvování tohoto předmětu nelze klasifikovat předmět 101MT02 Předmět je zařazen do následujících studijních plánů:- studijní plán Building Structures (BD201700_08), skupina Building Structures, Compulsory Subjects, 1st semester (BD20150100), dop. semestr 1 (valid from 2017-18 up to 2019-20 ) - studijní plán Civil Engineering (BD2020), skupina Building Structures, Compulsory Subjects, 1st semester (BD20200100), dop. semestr 1 (valid from 2020-21 )