Calculus 1

Course guarantor:

Pavel Strachota

Lecturer:

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. Review of high school mathematics: mathematical logic, equations and inequalities, trigonometric functions, exponential and logarithmic functions, summation and product notation, mathematical induction.

2. Sets and mappings.

3. Limit of real and complex sequences basic properties, limits of selected sequences, the number e and the exponential function, some elementary functions.

4. Limit and continuity of a function of one real variable basic properties.

5. Derivative of a function basic properties.

6. Fundamental theorems of differential calculus for real functions of one real variable.

7. Analysis of function behavior.

Syllabus of tutorials:

1. Review of high school mathematics

2. Mappings, boundedness of sets, supremum and infimum

3. Limits of sequences

4. Accumulation points

5. Limits of functions

6. Continuity

7. Derivatives and function behavior

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)