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Elements of Calculus

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Code Completion Credits Range Language
BI-ZMA Z,ZK 6 3P+2C Czech
The course cannot be taken simultaneously with:
Mathematical Analysis 1 (BI-MA1.21)
The course is a substitute for:
Mathematical Analysis 1 (BI-MA1.21)
Garant předmětu:
Tomáš Kalvoda (O_o)
Ivo Petr
Ivo Petr
Department of Applied Mathematics

Students acquire knowledge and understanding of the fundamentals of classical calculus so that they are able to apply mathematical way of thinking and reasoning and are able to use basic proof techniques. They get skills to practically handle functions of one variable in solving the problems in informatics. They understand the links between the integrals and sums of sequences. They are able to estimate lower or upper bounds of values of real functions and to handle simple asymptotic expressions.


The ability to think mathematically and knowledge of a high school mathematics.

Syllabus of lectures:

1. Introduction, real numbers, basic properties of functions.

2. Sequences and their limits.

3. Extended scales of infinity, small- and big-O notation, theta.

4. Limits.

5. Continuity, introduction to derivatives.

6. Derivatives and properties of derivatives.

7. Classical theorems (Rolle, mean value, etc.), l'Hospital's rule.

8. Taylor polynomials and approximation, error estimation, root finding (bisection, Newton's method), monotony, extremes and optimization.

9. Convexity, function graph, primitive function, substitution.

10. Integration by parts, partial fractions.

11. Definite integral (properties, Newton's formula).

12. Improper integral.

13. Uses of integrals.

14. Space and time complexity of algorithms.

Syllabus of tutorials:

1. Domain of a function.

2. Basic properties of functions.

3. Sequences.

4. Limits of functions.

5. Differentiating.

6. Tangents/normals, implicit differentiation, related rates.

7. Limits of functions.

8. Approximation, optimization.

9. Graphs of functions, primitive functions.

10. Indefinite integral.

11. Definite integral.

12. Improper integral.

13. Applications of integrals.

Study Objective:
Study materials:


Further information:
Time-table for winter semester 2022/2023:
Time-table is not available yet
Time-table for summer semester 2022/2023:
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The course is a part of the following study plans:
Data valid to 2023-03-24
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