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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2017/2018

Elements of Calculus

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Code Completion Credits Range Language
BI-ZMA Z,ZK 6 3+2 Czech
Lecturer:
Ivo Petr, Tomáš Kalvoda (guarantor), Daniel Vašata
Tutor:
Ivo Petr, Tomáš Kalvoda (guarantor), Dana Čermáková, Matyáš Hollmann, Pavel Hrabák, Martin Jureček, Václav Košík, Jakub Krásenský, Jan Mazáč, Petr Olšák, Petr Pauš, Eva Pernecká, 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
roomT9:301
Olšák P.
09:15–10:45
(parallel nr.103)
Dejvice
NBFIT učebna
roomT9:347
Zhouf J.
11:00–12:30
(parallel nr.102)
Dejvice
NBFIT učebna
roomTK:BS
Petr I.
12:45–14:15
ODD WEEK

(lecture parallel2)
Dejvice
NTK Ballingův sál
roomT9:347
Olšák P.
14:30–16:00
(parallel nr.205)
Dejvice
NBFIT učebna
roomT9:301
Petr I.
16:15–17:45
(parallel nr.101)
Dejvice
NBFIT učebna
roomT9:347
Zhouf J.
09:15–10:45
(parallel nr.204)
Dejvice
NBFIT učebna
roomT9:301
Olšák P.
11:00–12:30
(parallel nr.104)
Dejvice
NBFIT učebna
roomT9:346
Krásenský J.
12:45–14:15
(parallel nr.207)
Dejvice
NBFIT učebna
roomT9:346
Zhouf J.
14:30–16:00
(parallel nr.301)
Dejvice
NBFIT učebna
roomT9:346
Zhouf J.
16:15–17:45
(parallel nr.302)
Dejvice
NBFIT učebna
roomT9:302
Tichý J.
12:45–14:15
(parallel nr.208)
Dejvice
NBFIT učebna
Tue
roomT9:301
Mazáč J.
07:30–09:00
(parallel nr.112)
Dejvice
NBFIT učebna
roomT9:302
Čermáková D.
09:15–10:45
(parallel nr.203)
Dejvice
NBFIT učebna
roomTH:A-1242
Hrabák P.
11:00–12:30
(parallel nr.111)
Thákurova 7 (FSv-budova A)
roomTH:A-1342
Zahradová K.
14:30–16:00
(parallel nr.210)
Thákurova 7 (FSv-budova A)
roomT9:105
Kalvoda T.
18:00–19:30
ODD WEEK

(lecture parallel1)
Dejvice
Posluchárna
roomTH:A-1242
Hrabák P.
09:15–10:45
(parallel nr.209)
Thákurova 7 (FSv-budova A)
roomT9:105
Vašata D.
18:00–19:30
EVEN WEEK

(lecture parallel3)
Dejvice
Posluchárna
Fri
roomT9:346
Košík V.
07:30–09:00
(parallel nr.211)
Dejvice
NBFIT učebna
roomT9:301
Pernecká E.
09:15–10:45
(parallel nr.303)
Dejvice
NBFIT učebna
roomT9:302
Hollmann M.
11:00–12:30
(parallel nr.305)
Dejvice
NBFIT učebna
roomT9:302
Petr I.
14:30–16:00
(parallel nr.307)
Dejvice
NBFIT učebna
roomT4:D1-366
Petr I.
16:15–17:45
(lecture parallel2)
Dejvice
Posluchárna 366
roomT9:302
Mazáč J.
18:00–19:30
(parallel nr.201)
Dejvice
NBFIT učebna
roomT9:346
Košík V.
09:15–10:45
(parallel nr.304)
Dejvice
NBFIT učebna
roomT9:301
Pernecká E.
11:00–12:30
(parallel nr.306)
Dejvice
NBFIT učebna
roomT9:347
Semorádová I.
14:30–16:00
(parallel nr.308)
Dejvice
NBFIT učebna
roomTH:A-1442
Strmisková L.
16:15–17:45
(parallel nr.309)
Thákurova 7 (FSv-budova A)
roomTH:A-1342
Čermáková D.
18:00–19:30
(parallel nr.202)
Thákurova 7 (FSv-budova A)
roomT9:346
Kalvoda T.
14:30–16:00
(parallel nr.312)
Dejvice
NBFIT učebna
roomTH:A-1342
Čermáková D.
16:15–17:45
(parallel nr.310)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Strmisková L.
18:00–19:30
(parallel nr.206)
Thákurova 7 (FSv-budova A)
roomT9:347
Semorádová I.
16:15–17:45
(parallel nr.311)
Dejvice
NBFIT učebna
Thu
roomT9:105
Kalvoda T.
14:30–16:00
(lecture parallel1)
Dejvice
Posluchárna
roomT9:105
Vašata D.
16:15–17:45
(lecture parallel3)
Dejvice
Posluchárna
Fri
roomTH:A-1242
Jureček M.
07:30–09:00
(parallel nr.212)
Thákurova 7 (FSv-budova A)
roomTH:A-1342
Pauš P.
09:15–10:45
(parallel nr.105)
Thákurova 7 (FSv-budova A)
roomTH:A-1342
Pauš P.
11:00–12:30
(parallel nr.107)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Hollmann M.
12:45–14:15
(parallel nr.109)
Thákurova 7 (FSv-budova A)
roomTH:A-1242
Jureček M.
09:15–10:45
(parallel nr.106)
Thákurova 7 (FSv-budova A)
roomTH:A-1242
Zahradová K.
11:00–12:30
(parallel nr.108)
Thákurova 7 (FSv-budova A)
roomT9:302
Krásenský J.
12:45–14:15
(parallel nr.110)
Dejvice
NBFIT učebna
Time-table for summer semester 2017/2018:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2017-11-23
For updated information see http://bilakniha.cvut.cz/en/predmet1122106.html