Mathematics I.

Course guarantor:

Gejza Dohnal

Lecturer:

Tomáš Bodnár, Hynek Řezníček

Tutor:

Tomáš Bodnár, Hynek Řezníček

Supervisor:

Department of Technical Mathematics

Synopsis:

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.

Requirements:

Syllabus of lectures:

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.

Syllabus of tutorials:

Study Objective:

Study materials:

Engineering mathematics Eighth edition, Red Globe Press, Macmillan International Higher Education, London 2020

Note:

Time-table for winter semester 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue	roomKN:A-313 Bodnár T. 10:45–12:15 (lecture parallel1) Karlovo nám.
Wed	roomKN:A-313 Řezníček H. 09:00–10:30 (lecture parallel1 parallel nr.101) Karlovo nám.
Thu	roomKN:A-313 Bodnár T. 10:45–12:15 (lecture parallel1) Karlovo nám.
Fri	roomKN:A-313 Řezníček H. 10:45–12:15 (lecture parallel1 parallel nr.101) Karlovo nám.

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: