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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.

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.

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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