Mathematics I.

Course guarantor:

Gejza Dohnal

Lecturer:

Tomáš Bodnár, Hynek Řezníček

Tutor:

Tomáš Bodnár, Anna Lancmanová, 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 2025/2026:

	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	roomT4:C2-334 Bodnár T. 12:30–14:00 (lecture parallel1) Dejvice
Tue	roomT4:A1-505d Řezníček H. 09:00–10:30 (lecture parallel1 parallel nr.102) Dejvice roomT4:A1-505d Lancmanová A. 10:45–12:15 (lecture parallel1 parallel nr.101) Dejvice
Wed	roomT4:C2-334 Bodnár T. 14:15–15:45 (lecture parallel1) Dejvice
Thu
Fri	roomT4:A1-505d Lancmanová A. 09:00–10:30 (lecture parallel1 parallel nr.101) Dejvice roomT4:A1-505d Řezníček H. 12:30–14:00 (lecture parallel1 parallel nr.102) Dejvice

Time-table for summer semester 2025/2026:

Time-table is not available yet

The course is a part of the following study plans: