# Mathematics 3

Kód předmětu: 101MT03
Zakončení předmětu: Z,ZK
Počet kreditů: 6 kred.
Rozsah výuky: 3+2
Web předmětu: https://mat.fsv.cvut.cz/vyuka/bakalari/eng/zs/MT03/

Anotace (semestr ) 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. 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. Povinná literatura:   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 Doporučená literatura:   Sherman Stein, Anthony Barcellos, Calculus and Analytic Geometry 5th ed., Mcgraw-Hill 1992, ISBN 978-0070611757 Tento předmět lze klasifikovat až po klasifikaci předmětu 101MT02 Předmět je zařazen do následujících studijních plánů:- studijní plán Building Structures (BD201700_08), skupina Building structures, Compulsory Subjects, 3rd semester (BD20150300), dop. semestr 3 (valid from 2017-18 up to 2019-20 ) - studijní plán Civil Engineering (BD2020), skupina Building Structures, Compulsory Subjects, 3rd semester (BD20200300), dop. semestr 3 (valid from 2020-21 )