Elements of Calculus
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| BI-ZMA | Z,ZK | 6 | 3+2 | Czech |
- Lecturer:
- Tomáš Kalvoda (guarantor), Ivo Petr, Daniel Vašata
- Tutor:
- Tomáš Kalvoda (guarantor), Dana Čermáková, Matyáš Hollmann, Pavel Hrabák, Martin Jureček, Václav Košík, Jakub Krásenský, Jan Mazáč, Petr Olšák, Petr Pauš, Eva Pernecká, Ivo Petr, Iveta Semorádová, Lucie Strmisková, Jakub Tichý (Štěpán), Kateřina Zahradová, 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:
- Syllabus of lectures:
-
1. Introduction, real numbers, basic properties of functions.
2. Limits.
3. Continuity, introduction to derivatives.
4. Properties of derivatives, implicit differentiation, numerical and symbolic differentiation on a computer.
5. Classical theorems (Rolle, mean value, etc.), differentiation using limits, finding limits using derivatives (l?Hospital?s rule).
6. Taylor polynomials and approximation, error estimation, root finding (bisection, regula falsi, Newton?s method), monotony, extremes and optimization.
7. Convexity, function graph, primitive function, substitution.
8. Integration by parts, partial fractions.
9. Definite integral (properties, N-L formula).
10. Improper integral.
11. Uses of integrals, numerical methods for definite integrals.
12. Sequences and their limits.
13. Extended scales of infinity, small- and big-O notation, theta.
14. Space and time complexity of algorithms.
- Syllabus of tutorials:
-
1. Domain of a function.
2. Basic properties of functions.
3. Limits of functions.
4. Differentiating.
5. Tangents/normals, implicit differentiation, related rates.
6. Limits of functions.
7. Approximation, optimization.
8. Graphs of functions, primitive functions.
9. Indefinite integral.
10. Definite integral.
11. Improper integral.
12. Applications of integrals.
13. Sequences.
14. Assessment.
- Study Objective:
- Study materials:
-
1.
- Note:
- Time-table for winter semester 2017/2018:
-
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 2017/2018:
- Time-table is not available yet
- The course is a part of the following study plans:
-
- Information Technology - Version for those who Enrolled in 2012 (in Czech) (compulsory course in the program)
- Informatics (Bachelor)- Version for those who Enrolled in 2013 (in Czech) (compulsory course in the program)
- Web and Multimedia- Version for those who Enrolled in 2013 (in Czech) (compulsory course in the program)
- Computer Science - Version for those who Enrolled in 2013 (in Czech) (compulsory course in the program)
- Information Technology - Version for those who Enrolled in 2013 (in Czech) (compulsory course in the program)
- Software Engineering- Version for those who Enrolled in 2013 (in Czech) (compulsory course in the program)
- Information Systems and Management - Version for those who Enrolled in 2013 (in Czech) (compulsory course in the program)
- Informatics (Bachelor)- Version for those who Enrolled in 2014 (in Czech) (compulsory course in the program)
- Web and Multimedia- Version for those who Enrolled in 2014 (in Czech) (compulsory course in the program)
- Computer Science - Version for those who Enrolled in 2014 (in Czech) (compulsory course in the program)
- Information Technology - Version for those who Enrolled in 2014 (in Czech) (compulsory course in the program)
- Computer Engineering, Version for those who Enrolled in 2014, in Czech (compulsory course in the program)
- Software Engineering- Version for those who Enrolled in 2014 (in Czech) (compulsory course in the program)
- Information Systems and Management - Version for those who Enrolled in 2014 (in Czech) (compulsory course in the program)
- Bc. Programme Informatics, in Czech, Version 2015, 2016, 2017 and 2018 (compulsory course in the program)
- Bc. Branch Security and Information Technology, in Czech, Version 2015, 2016, 2017 and 2018 (compulsory course in the program)
- Bc. Branch Computer Science, in Czech, Version 2015, 2016, 2017 and 2018 (compulsory course in the program)
- Bc. Branch Computer Engineering, in Czech, Version 2015, 2016, 2017 and 2018 (compulsory course in the program)
- Bachelor Branch Information Systems and Management, in Czech, Version 2015, 2016, 2017 and 2018 (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 2016, 2017 and 2018 (compulsory course in the program)
- Bachelor Branch, Specialization Web Engineering, in Czech, Version 2015 2016, 2017 and 2018 (compulsory course in the program)
- Bachelor Branch WSI, Specialization Computer Grafics, in Czech, Version 2015, 2016, 2017 and 2018 (compulsory course in the program)
- Bachelor Branch Knowledge Engineering, in Czech, Version 2018 (compulsory course in the program)