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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2020/2021

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), Pavel Hrabák, 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
roomT9:343
Zhouf J.
12:45–14:15
EVEN WEEK

(parallel nr.21)
Dejvice
NBFIT učebna
roomT9:343
Zhouf J.
14:30–16:00
EVEN WEEK

(parallel nr.22)
Dejvice
NBFIT učebna
roomT9:343
Olšák P.
16:15–17:45
EVEN WEEK

(parallel nr.23)
Dejvice
NBFIT učebna
roomT9:343
Olšák P.
18:00–19:30
EVEN WEEK

(parallel nr.24)
Dejvice
NBFIT učebna
roomT9:343
Zhouf J.
12:45–14:15
ODD WEEK

(parallel nr.1)
Dejvice
NBFIT učebna
roomT9:343
Zhouf J.
14:30–16:00
ODD WEEK

(parallel nr.2)
Dejvice
NBFIT učebna
roomT9:343
Olšák P.
16:15–17:45
ODD WEEK

(parallel nr.3)
Dejvice
NBFIT učebna
roomT9:343
Olšák P.
18:00–19:30
ODD WEEK

(parallel nr.4)
Dejvice
NBFIT učebna
roomT9:105
Hrabák P.
14:30–16:00
EVEN WEEK

(lecture parallel2)
Dejvice
Posluchárna
roomT9:105
Kalvoda T.
14:30–16:00
ODD WEEK

(lecture parallel1)
Dejvice
Posluchárna
Tue
roomT9:155
Petr I.
16:15–17:45
EVEN WEEK

(lecture parallel3)
Dejvice
Posluchárna
Fri
roomT9:347
Slavík J.
07:30–09:00
EVEN WEEK

(parallel nr.25)
Dejvice
NBFIT učebna
roomT9:155
Petr I.
11:00–12:30
(lecture parallel3)
Dejvice
Posluchárna
roomTH:A-942
Šolc J.
12:45–14:15
EVEN WEEK

(parallel nr.29)
Thákurova 7 (FSv-budova A)
roomTH:A-942
Šolc J.
14:30–16:00
EVEN WEEK

(parallel nr.30)
Thákurova 7 (FSv-budova A)
roomTH:A-942
Strmisková L.
16:15–17:45
EVEN WEEK

(parallel nr.31)
Thákurova 7 (FSv-budova A)
roomTH:A-942
Strmisková L.
18:00–19:30
ODD WEEK

(parallel nr.12)
Thákurova 7 (FSv-budova A)
roomTH:A-1242
Kalvoda T.
07:30–09:00
EVEN WEEK

(parallel nr.26)
Thákurova 7 (FSv-budova A)
roomT9:347
Slavík J.
09:15–10:45
EVEN WEEK

(parallel nr.27)
Dejvice
NBFIT učebna
roomTH:A-942
Šolc J.
12:45–14:15
ODD WEEK

(parallel nr.9)
Thákurova 7 (FSv-budova A)
roomTH:A-942
Šolc J.
14:30–16:00
ODD WEEK

(parallel nr.10)
Thákurova 7 (FSv-budova A)
roomTH:A-942
Strmisková L.
16:15–17:45
ODD WEEK

(parallel nr.11)
Thákurova 7 (FSv-budova A)
roomTH:A-942
Strmisková L.
18:00–19:30
EVEN WEEK

(parallel nr.32)
Thákurova 7 (FSv-budova A)
roomT9:347
Slavík J.
07:30–09:00
ODD WEEK

(parallel nr.5)
Dejvice
NBFIT učebna
roomTH:A-942
Zhouf J.
09:15–10:45
EVEN WEEK

(parallel nr.28)
Thákurova 7 (FSv-budova A)
roomTH:A-942
Zhouf J.
11:00–12:30
ODD WEEK

(parallel nr.13)
Thákurova 7 (FSv-budova A)
roomTH:A-1242
Kalvoda T.
07:30–09:00
ODD WEEK

(parallel nr.6)
Thákurova 7 (FSv-budova A)
roomTH:A-942
Zhouf J.
09:15–10:45
ODD WEEK

(parallel nr.8)
Thákurova 7 (FSv-budova A)
roomTH:A-942
Zhouf J.
11:00–12:30
EVEN WEEK

(parallel nr.33)
Thákurova 7 (FSv-budova A)
roomT9:105
Hrabák P.
07:30–09:00
(lecture parallel2)
Dejvice
Posluchárna
roomT9:347
Slavík J.
09:15–10:45
ODD WEEK

(parallel nr.7)
Dejvice
NBFIT učebna
Thu
roomTH:A-942
Pauš P.
09:15–10:45
EVEN WEEK

(parallel nr.34)
Thákurova 7 (FSv-budova A)
roomTH:A-1247

18:00–19:30
ODD WEEK

(parallel nr.17)
Thákurova 7 (FSv-budova A)
seminární místnost
roomTH:A-942
Pauš P.
09:15–10:45
ODD WEEK

(parallel nr.14)
Thákurova 7 (FSv-budova A)
roomTH:A-942
Pauš P.
11:00–12:30
EVEN WEEK

(parallel nr.35)
Thákurova 7 (FSv-budova A)
roomT9:346
Pauš P.
14:30–16:00
EVEN WEEK

(parallel nr.36)
Dejvice
NBFIT učebna
roomTH:A-1247

18:00–19:30
EVEN WEEK

(parallel nr.37)
Thákurova 7 (FSv-budova A)
seminární místnost
roomTH:A-942
Pauš P.
11:00–12:30
ODD WEEK

(parallel nr.15)
Thákurova 7 (FSv-budova A)
roomT9:105
Kalvoda T.
14:30–16:00
(lecture parallel1)
Dejvice
Posluchárna
roomT9:346
Pauš P.
14:30–16:00
ODD WEEK

(parallel nr.16)
Dejvice
NBFIT učebna
Fri
roomT9:346

07:30–09:00
ODD WEEK

(parallel nr.18)
Dejvice
NBFIT učebna
roomT9:347
Olšák P.
11:00–12:30
ODD WEEK

(parallel nr.19)
Dejvice
NBFIT učebna
roomT9:347
Olšák P.
12:45–14:15
ODD WEEK

(parallel nr.20)
Dejvice
NBFIT učebna
roomT9:346

07:30–09:00
EVEN WEEK

(parallel nr.38)
Dejvice
NBFIT učebna
roomT9:347
Olšák P.
11:00–12:30
EVEN WEEK

(parallel nr.39)
Dejvice
NBFIT učebna
roomT9:347
Olšák P.
12:45–14:15
EVEN WEEK

(parallel nr.40)
Dejvice
NBFIT učebna
Time-table for summer semester 2020/2021:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-09-26
For updated information see http://bilakniha.cvut.cz/en/predmet1122106.html