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Mathematics I. (E011091)
 Departments: ústav technické matematiky (12101) Abbreviation: MA1EN Approved: 24.03.2022 Valid until: ?? Range: 4P+4C+0L Semestr: Credits: 7 Completion: Z,ZK Language: EN
Annotation
Basics of linear algebra - vectors, vector spaces, linear dependence and independence of vectors, dimension, basis.
Matrix, operation, rank. Determinant. Regular and singular matrices, inverse matrix.
Systems of linear equations, Frobeni's theorem, Gaussian elimination method.
Eigenvalues and eigenvectors of a matrix.
Differential calculus of functions of one variable. Sequences, monotonicity, limit.
Limit and continuity of a function. Derivation, geometric and physical meaning.
Monotonicity of a function, inflection point. Asymptotes, examination of course of a function, graph of a function.
Taylor polynomial, the remainder after the nth power. Approximate solution of the equation f(x)=0.
Integral calculus of functions of one variable – indefinite integral, integration per-partes, substitutions.
Definite integral, calculation.
Application of a definite integral: area surface, volume of a rotating body, length of a curve, application in mechanics.
Numerical calculation of the integral.
Improper integral.
Teacher's
doc. Ing. Tomáš Bodnár Ph.D.
Zimní 2023/2024
doc. Ing. Tomáš Bodnár Ph.D.
Zimní 2022/2023
Structure
Basics of linear algebra - vectors, vector spaces, linear dependence and independence of vectors, dimension, basis.
Matrix, operation, rank. Determinant. Regular and singular matrices, inverse matrix.
Systems of linear equations, Frobeni's theorem, Gaussian elimination method.
Eigenvalues and eigenvectors of a matrix.
Differential calculus of functions of one variable. Sequences, monotonicity, limit.
Limit and continuity of a function. Derivation, geometric and physical meaning.
Monotonicity of a function, inflection point. Asymptotes, examination of course of a function, graph of a function.
Taylor polynomial, the remainder after the nth power. Approximate solution of the equation f(x)=0.
Integral calculus of functions of one variable – indefinite integral, integration per-partes, substitutions.
Definite integral, calculation.
Application of a definite integral: area surface, volume of a rotating body, length of a curve, application in mechanics.
Numerical calculation of the integral.
Improper integral.
Literarture
Engineering mathematics Eighth edition, Red Globe Press, Macmillan International Higher Education, London 2020
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