CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

# Mathematics I.

Code Completion Credits Range Language
E011091 Z,ZK 7 4P+4C+0L English
Garant předmětu:
Tomáš Bodnár
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 2023/2024:
 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 roomKN:A-404Řezníček H.09:00–10:30(lecture parallel1parallel nr.101)Karlovo nám.Posluchárna KA404 roomKN:A-313Bodnár T.12:30–14:00(lecture parallel1)Karlovo nám.Učebna KA313roomKN:A-31314:15–15:45(lecture parallel1parallel nr.102)Karlovo nám.Učebna KA313 roomKN:A-215Bodnár T.09:00–10:30(lecture parallel1)Karlovo nám.Posluchárna KA215roomKN:A-215Řezníček H.12:30–14:00(lecture parallel1parallel nr.101)Karlovo nám.Posluchárna KA215 roomKN:A-21510:45–12:15(lecture parallel1parallel nr.102)Karlovo nám.Posluchárna KA215
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2023-08-30
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