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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2016/2017

Elements of Calculus

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Code Completion Credits Range Language
BI-ZMA Z,ZK 6 3+2 Czech
Lecturer:
Tomáš Kalvoda (guarantor), Daniel Vašata
Tutor:
Tomáš Kalvoda (guarantor), Dana Čermáková, Lenka Háková, Pavel Hrabák, Kateřina Medková, Marta Pavelka, Jakub Slavík, Filip Soudský, Lucie Strmisková, Irena Šindelářová, Jakub Šolc, Jakub Tichý (Štěpán), 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:
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 2016/2017:
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
roomT9:302
Slavík J.
09:15–10:45
(lecture parallel1
parallel nr.101)

Dejvice
NBFIT učebna
roomT9:301
Kalvoda T.
11:00–12:30
(lecture parallel1
parallel nr.102)

Dejvice
NBFIT učebna
roomT9:301
Kalvoda T.
12:45–14:15
(lecture parallel1
parallel nr.103)

Dejvice
NBFIT učebna
roomTH:A-1342
Háková L.
14:30–16:00
(lecture parallel1
parallel nr.104)

Thákurova 7 (FSv-budova A)
roomT9:301
Soudský F.
16:15–17:45
(lecture parallel1
parallel nr.105)

Dejvice
NBFIT učebna
roomT9:301
Šindelářová I.
18:00–19:30
(lecture parallel1
parallel nr.106)

Dejvice
NBFIT učebna
roomTH:A-1442
Soudský F.
09:15–10:45
(lecture parallel2
parallel nr.204)

Thákurova 7 (FSv-budova A)
roomT9:302
Slavík J.
11:00–12:30
(lecture parallel1
parallel nr.210)

Dejvice
NBFIT učebna
roomTH:A-1242
Hrabák P.
12:45–14:15
(lecture parallel1
parallel nr.206)

Thákurova 7 (FSv-budova A)
roomT9:301
Soudský F.
14:30–16:00
(lecture parallel3
parallel nr.205)

Dejvice
NBFIT učebna
roomTH:A-1242
Hrabák P.
16:15–17:45
(lecture parallel2
parallel nr.208)

Thákurova 7 (FSv-budova A)
roomT9:302
Zhouf J.
18:00–19:30
(lecture parallel3
parallel nr.302)

Dejvice
NBFIT učebna
roomTH:A-1342
Hrabák P.
09:15–10:45
(lecture parallel1
parallel nr.113)

Thákurova 7 (FSv-budova A)
roomTH:A-1442
Soudský F.
11:00–12:30
(lecture parallel3
parallel nr.308)

Thákurova 7 (FSv-budova A)
roomT9:302
Zhouf J.
12:45–14:15
(lecture parallel3
parallel nr.309)

Dejvice
NBFIT učebna
roomT9:302
Zhouf J.
14:30–16:00
(lecture parallel2
parallel nr.207)

Dejvice
NBFIT učebna
Tue
roomTH:A-1342
Čermáková D.
07:30–09:00
(lecture parallel2
parallel nr.211)

Thákurova 7 (FSv-budova A)
roomTH:A-1342
Čermáková D.
09:15–10:45
(lecture parallel1
parallel nr.107)

Thákurova 7 (FSv-budova A)
roomTH:A-1442
Vašata D.
12:45–14:15
(lecture parallel1
parallel nr.112)

Thákurova 7 (FSv-budova A)
Fri
roomTH:A-1442
Strmisková L.
07:30–09:00
(lecture parallel1
parallel nr.108)

Thákurova 7 (FSv-budova A)
roomTH:A-1442
Strmisková L.
09:15–10:45
(lecture parallel1
parallel nr.109)

Thákurova 7 (FSv-budova A)
roomT9:105
Kalvoda T.
11:00–12:30
(lecture parallel1)
Dejvice
Posluchárna
roomTH:A-1342
Kalvoda T.
14:30–16:00
(lecture parallel3
parallel nr.307)

Thákurova 7 (FSv-budova A)
roomT9:105
Vašata D.
09:15–10:45
(lecture parallel3)
Dejvice
Posluchárna
Thu
roomTH:A-1442
Čermáková D.
11:00–12:30
(lecture parallel3
parallel nr.306)

Thákurova 7 (FSv-budova A)
roomT9:105
Kalvoda T.
14:30–16:00
ODD WEEK

(lecture parallel1)
Dejvice
Posluchárna
roomT9:155
Kalvoda T.
16:15–17:45
EVEN WEEK

(lecture parallel2)
Dejvice
Posluchárna
roomT9:347
Vašata D.
18:00–19:30
(lecture parallel3
parallel nr.203)

Dejvice
NBFIT učebna
roomT9:302
Háková L.
14:30–16:00
(lecture parallel2
parallel nr.209)

Dejvice
NBFIT učebna
roomT9:105
Vašata D.
14:30–16:00
EVEN WEEK

(lecture parallel3)
Dejvice
Posluchárna
Fri
roomT9:346
Tichý J.
07:30–09:00
(lecture parallel3
parallel nr.310)

Dejvice
NBFIT učebna
roomTH:A-1242
Šolc J.
09:15–10:45
(lecture parallel2
parallel nr.201)

Thákurova 7 (FSv-budova A)
roomT9:155
Kalvoda T.
11:00–12:30
(lecture parallel2)
Dejvice
Posluchárna
roomTH:A-1242
Brzicová M.
12:45–14:15
(lecture parallel2
parallel nr.202)

Thákurova 7 (FSv-budova A)
roomTH:A-1242
Šindelářová I.
14:30–16:00
(lecture parallel1
parallel nr.110)

Thákurova 7 (FSv-budova A)
roomTH:A-1242
Šolc J.
07:30–09:00
(lecture parallel3
parallel nr.311)

Thákurova 7 (FSv-budova A)
roomT9:302
Soudský F.
09:15–10:45
(lecture parallel3
parallel nr.305)

Dejvice
NBFIT učebna
roomTH:A-1242
Brzicová M.
11:00–12:30
(lecture parallel3
parallel nr.301)

Thákurova 7 (FSv-budova A)
roomT9:347
Medková K.
12:45–14:15
(lecture parallel3
parallel nr.303)

Dejvice
NBFIT učebna
roomT9:347
Medková K.
14:30–16:00
(lecture parallel1
parallel nr.111)

Dejvice
NBFIT učebna
roomT9:302
Soudský F.
11:00–12:30
(lecture parallel3
parallel nr.304)

Dejvice
NBFIT učebna
Time-table for summer semester 2016/2017:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2017-09-24
For updated information see http://bilakniha.cvut.cz/en/predmet1122106.html