Calculus 2

Course guarantor:

Edita Pelantová

Lecturer:

Pavel Eichler, Petr Kubera

Tutor:

Pavel Eichler, Petr Kubera

Supervisor:

Department of Software Engineering

Synopsis:

Requirements:

Conditions for credit are: a maximum of 8 absences and at least one-third of the points from mini-tests.

The exam is oral, with primary emphasis on formulating problems and understanding basic concepts, including the principles of the relevant mathematical theorems and statements.

Syllabus of lectures:

1. Continuation of differential calculus: Taylors formula, Taylor polynomials

2. Numerical series: Convergence criteria, absolute and conditional convergence, operations with series

3. Integral calculus: Antiderivatives, integration methods, definite integral (Riemann definition) and its applications, improper Riemann integral

4. Power series (in real and complex domains): CauchyHadamard theorem, expansion of a real function into a power series, determination of the series sum

Syllabus of tutorials:

1. Calculation of limits using LHospitals rule

2. Function approximation using Taylor polynomials

3. Convergence of series

4. Finding antiderivatives

5. Calculation of areas and volumes

6. Expansion of a function into a power series

Study Objective:

Study materials:

Note:

Time-table for winter semester 2025/2026:

Time-table is not available yet

Time-table for summer semester 2025/2026:

Time-table is not available yet

The course is a part of the following study plans:

• Applications of Informatics in Natural Sciences (compulsory course in the program)