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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2018/2019

Elements of Calculus

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Code Completion Credits Range Language
BI-ZMA Z,ZK 6 3+2 Czech
Lecturer:
Jitka Hrabáková, Tomáš Kalvoda (guarantor), Ivo Petr
Tutor:
Jitka Hrabáková, Tomáš Kalvoda (guarantor), Dana Čermáková, Pavel Hrabák, Martin Jureček, Jan Mazáč, Petr Olšák, Petr Pauš, Ivo Petr, Lucie Strmisková, František Štampach, Jakub Tichý (Štěpán), 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 2018/2019:
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
roomT9:301
Zhouf J.
11:00–12:30
(parallel nr.208)
Dejvice
NBFIT učebna
roomT9:105
Kalvoda T.
14:30–16:00
EVEN WEEK

(lecture parallel1)
Dejvice
Posluchárna
roomT9:301
Zhouf J.
16:15–17:45
(parallel nr.101)
Dejvice
NBFIT učebna
roomT9:301
Zhouf J.
18:00–19:30
(parallel nr.102)
Dejvice
NBFIT učebna
roomTK:BS
Hrabáková J.
11:00–12:30
ODD WEEK

(lecture parallel3)
Dejvice
NTK Ballingův sál
roomTH:A-1442
Zhouf J.
12:45–14:15
(parallel nr.108)
Thákurova 7 (FSv-budova A)
roomT9:105
Petr I.
14:30–16:00
ODD WEEK

(lecture parallel2)
Dejvice
Posluchárna
roomT9:302
Kalvoda T.
16:15–17:45
(parallel nr.301)
Dejvice
NBFIT učebna
roomT9:346
Hrabáková J.
18:00–19:30
(parallel nr.302)
Dejvice
NBFIT učebna
roomT9:302
Petr I.
12:45–14:15
(parallel nr.303)
Dejvice
NBFIT učebna
roomTK:BS
Hrabáková J.
14:30–16:00
(lecture parallel3)
Dejvice
NTK Ballingův sál
Tue
roomT9:346
Mazáč J.
07:30–09:00
(parallel nr.103)
Dejvice
NBFIT učebna
roomT9:346
Mazáč J.
09:15–10:45
(parallel nr.104)
Dejvice
NBFIT učebna
roomTH:A-1342
Zhouf J.
11:00–12:30
(parallel nr.105)
Thákurova 7 (FSv-budova A)
roomT9:302
Čermáková D.
16:15–17:45
(parallel nr.106)
Dejvice
NBFIT učebna
roomT9:302
Čermáková D.
18:00–19:30
(parallel nr.107)
Dejvice
NBFIT učebna
roomTH:A-1442
Jureček M.
09:15–10:45
(parallel nr.304)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Olšák P.
16:15–17:45
(parallel nr.109)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Olšák P.
18:00–19:30
(parallel nr.110)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Jureček M.
11:00–12:30
(parallel nr.305)
Thákurova 7 (FSv-budova A)
roomT9:302
Čermáková D.
14:30–16:00
(parallel nr.213)
Dejvice
NBFIT učebna
roomTH:A-1242
Petr I.
12:45–14:15
(parallel nr.306)
Thákurova 7 (FSv-budova A)
Fri
roomT9:105
Petr I.
07:30–09:00
(lecture parallel2)
Dejvice
Posluchárna
roomT9:346
Petr I.
09:15–10:45
(parallel nr.201)
Dejvice
NBFIT učebna
roomT9:302
Tichý J.
14:30–16:00
(parallel nr.202)
Dejvice
NBFIT učebna
roomTH:A-1342
Strmisková L.
16:15–17:45
(parallel nr.203)
Thákurova 7 (FSv-budova A)
roomTH:A-1342
Strmisková L.
18:00–19:30
(parallel nr.204)
Thákurova 7 (FSv-budova A)
roomT9:346
Tichý J.
07:30–09:00
(parallel nr.207)
Dejvice
NBFIT učebna
Thu
roomT9:347
Kalvoda T.
11:00–12:30
(parallel nr.307)
Dejvice
NBFIT učebna
roomT9:105
Kalvoda T.
14:30–16:00
(lecture parallel1)
Dejvice
Posluchárna
roomT9:347
Hrabák P.
18:00–19:30
(parallel nr.212)
Dejvice
NBFIT učebna
roomTH:A-1442
Štampach F.
12:45–14:15
(parallel nr.206)
Thákurova 7 (FSv-budova A)
roomT9:347
Hrabák P.
14:30–16:00
(parallel nr.205)
Dejvice
NBFIT učebna
roomT9:347
Hrabák P.
16:15–17:45
(parallel nr.310)
Dejvice
NBFIT učebna
roomT9:347
Kalvoda T.
12:45–14:15
(parallel nr.308)
Dejvice
NBFIT učebna
roomTH:A-1442
Štampach F.
14:30–16:00
(parallel nr.309)
Thákurova 7 (FSv-budova A)
Fri
roomT9:302
Olšák P.
07:30–09:00
(parallel nr.209)
Dejvice
NBFIT učebna
roomTH:A-1242
Pauš P.
09:15–10:45
(parallel nr.111)
Thákurova 7 (FSv-budova A)
roomTH:A-1242
Pauš P.
11:00–12:30
(parallel nr.112)
Thákurova 7 (FSv-budova A)
roomT9:346
Olšák P.
12:45–14:15
(parallel nr.113)
Dejvice
NBFIT učebna
roomT9:302
Olšák P.
09:15–10:45
(parallel nr.210)
Dejvice
NBFIT učebna
roomTH:A-1242
Pauš P.
12:45–14:15
(parallel nr.211)
Thákurova 7 (FSv-budova A)
Time-table for summer semester 2018/2019:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2018-10-20
For updated information see http://bilakniha.cvut.cz/en/predmet1122106.html