Elements of Calculus
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| BI-ZMA | Z,ZK | 6 | 3P+2C | Czech |
- Lecturer:
- Tomáš Kalvoda (guarantor), Pavel Hrabák, Karel Klouda, Ivo Petr
- Tutor:
- Tomáš Kalvoda (guarantor), Pavel Hrabák, Karel Klouda, Petr Olšák, Petr Pauš, Ivo Petr, Jakub Slavík, Lucie Strmisková, Jakub Šolc, Jaroslav Zhouf
- Supervisor:
- Department of Applied Mathematics
- Synopsis:
-
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.
- Requirements:
-
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:
-
1.
- Note:
- Further information:
- https://courses.fit.cvut.cz/BI-ZMA/
- Time-table for winter semester 2020/2021:
-
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 Tue Fri Thu Fri - Time-table for summer semester 2020/2021:
- Time-table is not available yet
- The course is a part of the following study plans:
-
- Bc. Programme Informatics, in Czech, Version 2015 to 2020 (compulsory course in the program)
- Bc. Branch Security and Information Technology, in Czech, Version 2015 to 2020 (compulsory course in the program)
- Bc. Branch Computer Science, in Czech, Version 2015 to 2020 (compulsory course in the program)
- Bc. Branch Computer Engineering, in Czech, Version 2015 to 2020 (compulsory course in the program)
- Bachelor Branch Information Systems and Management, in Czech, Version 2015 to 2020 (compulsory course in the program)
- Bachelor Branch Knowledge Engineering, in Czech, Version 2015, 2016 and 2017 (compulsory course in the program)
- Bachelor Branch WSI, Specialization Software Engineering, in Czech, Version 2015 to 2020 (compulsory course in the program)
- Bachelor Branch, Specialization Web Engineering, in Czech, Version 2015 to 2020 (compulsory course in the program)
- Bachelor Branch WSI, Specialization Computer Grafics, in Czech, Version 2015 to 2020 (compulsory course in the program)
- Bachelor Branch Knowledge Engineering, in Czech, Version 2018 to 2020 (compulsory course in the program)