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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Elements of Calculus

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Code Completion Credits Range Language
BI-ZMA Z,ZK 6 3P+2C Czech
Lecturer:
Tomáš Kalvoda (guarantor), Pavel Hrabák, Ivo Petr
Tutor:
Tomáš Kalvoda (guarantor), Dana Čermáková, Pavel Hrabák, Petr Olšák, Petr Pauš, Eva Pernecká, Ivo Petr, Lucie Strmisková, Daniel Štěrba, Daniel Vašata, 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 2019/2020:
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
roomTK:BS
Hrabák P.
09:15–10:45
(lecture parallel3)
Dejvice
NTK Ballingův sál
roomT9:343
Zhouf J.
11:00–12:30
(parallel nr.24)
Dejvice
NBFIT učebna
roomTH:A-1247
Hrabák P.
12:45–14:15
(parallel nr.2)
Thákurova 7 (FSv-budova A)
seminární místnost
roomT9:105
Petr I.
14:30–16:00
EVEN WEEK

(lecture parallel2)
Dejvice
Posluchárna
roomTH:A-1247
Zhouf J.
16:15–17:45
(parallel nr.27)
Thákurova 7 (FSv-budova A)
seminární místnost
roomT9:343
Strmisková L.
18:00–19:30
(parallel nr.5)
Dejvice
NBFIT učebna
roomTH:A-s135
Kalvoda T.
11:00–12:30
(parallel nr.1)
Thákurova 7 (FSv-budova A)
As135
roomT9:105
Kalvoda T.
14:30–16:00
ODD WEEK

(lecture parallel1)
Dejvice
Posluchárna
roomT9:343
Strmisková L.
16:15–17:45
(parallel nr.4)
Dejvice
NBFIT učebna
roomTH:A-1247
Zhouf J.
18:00–19:30
(parallel nr.28)
Thákurova 7 (FSv-budova A)
seminární místnost
roomT9:343
Zhouf J.
12:45–14:15
(parallel nr.25)
Dejvice
NBFIT učebna
Tue
roomTH:A-1442
Olšák P.
07:30–09:00
(parallel nr.6)
Thákurova 7 (FSv-budova A)
roomT9:302
Vašata D.
11:00–12:30
(parallel nr.30)
Dejvice
NBFIT učebna
roomTH:A-1247
Pauš P.
16:15–17:45
(parallel nr.9)
Thákurova 7 (FSv-budova A)
seminární místnost
roomTH:A-1442
Olšák P.
09:15–10:45
(parallel nr.7)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Hrabák P.
11:00–12:30
(parallel nr.8)
Thákurova 7 (FSv-budova A)
roomTK:BS
Hrabák P.
14:30–16:00
EVEN WEEK

(lecture parallel3)
Dejvice
NTK Ballingův sál
roomTH:A-1342
Zhouf J.
09:15–10:45
(parallel nr.29)
Thákurova 7 (FSv-budova A)
roomT9:302
Vašata D.
12:45–14:15
(parallel nr.34)
Dejvice
NBFIT učebna
Fri
roomT9:105
Petr I.
07:30–09:00
(lecture parallel2)
Dejvice
Posluchárna
roomTH:A-1247
Pernecká E.
09:15–10:45
(parallel nr.12)
Thákurova 7 (FSv-budova A)
seminární místnost
roomTH:A-1247
Pernecká E.
11:00–12:30
(parallel nr.13)
Thákurova 7 (FSv-budova A)
seminární místnost
roomTH:A-942
Pauš P.
14:30–16:00
(parallel nr.14)
Thákurova 7 (FSv-budova A)
roomT9:343
Petr I.
09:15–10:45
(parallel nr.31)
Dejvice
NBFIT učebna
roomTH:A-942
Kalvoda T.
11:00–12:30
(parallel nr.32)
Thákurova 7 (FSv-budova A)
roomTH:A-942
Pauš P.
12:45–14:15
(parallel nr.33)
Thákurova 7 (FSv-budova A)
Thu
roomT9:346
Štěrba D.
07:30–09:00
(parallel nr.15)
Dejvice
NBFIT učebna
roomT9:105
Kalvoda T.
14:30–16:00
(lecture parallel1)
Dejvice
Posluchárna
roomT9:346
Čermáková D.
16:15–17:45
(parallel nr.18)
Dejvice
NBFIT učebna
roomT9:346
Čermáková D.
18:00–19:30
(parallel nr.19)
Dejvice
NBFIT učebna
roomT9:346
Štěrba D.
09:15–10:45
(parallel nr.16)
Dejvice
NBFIT učebna
roomTH:A-s135
Kalvoda T.
12:45–14:15
(parallel nr.17)
Thákurova 7 (FSv-budova A)
As135
roomT9:347
Kalvoda T.
16:15–17:45
(parallel nr.35)
Dejvice
NBFIT učebna
Fri
roomTH:A-1342
Olšák P.
07:30–09:00
(parallel nr.20)
Thákurova 7 (FSv-budova A)
roomTH:A-1342
Olšák P.
09:15–10:45
(parallel nr.21)
Thákurova 7 (FSv-budova A)
roomTH:A-1342
Olšák P.
11:00–12:30
(parallel nr.22)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Petr I.
12:45–14:15
(parallel nr.23)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Petr I.
09:15–10:45
(parallel nr.36)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Petr I.
11:00–12:30
(parallel nr.37)
Thákurova 7 (FSv-budova A)
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2019-10-18
For updated information see http://bilakniha.cvut.cz/en/predmet1122106.html