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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2011/2012

Elemnts of calculus

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Code Completion Credits Range Language
BI-ZMA Z,ZK 6 3+2 Czech
Lecturer:
Edita Pelantová (gar.), Tomáš Kalvoda
Tutor:
Tomáš Bartoň, Dana Čermáková, Tomáš Kalvoda, Kateřina Marková, Jaroslav Milota, Ivo Petr, Barbora Planková, Ondřej Polívka, Václav Remeš, Tomáš Řehořek, Josef Schmidt, Pavel Strachota
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 2011/2012:
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
Remeš V.
09:15–10:45
(parallel nr.209)
Dejvice
NBFIT učebna
roomT9:302
Remeš V.
11:00–12:30
(lecture parallel2
parallel nr.208)

Dejvice
NBFIT učebna
roomT9:301
Planková B.
12:45–14:15
(lecture parallel2
parallel nr.207)

Dejvice
NBFIT učebna
roomT9:347
Planková B.
14:30–16:00
(lecture parallel2
parallel nr.213)

Dejvice
NBFIT učebna
roomT9:347
Řehořek T.
16:15–17:45
(lecture parallel2
parallel nr.210)

Dejvice
NBFIT učebna
Tue
roomT9:302
Strachota P.
07:30–09:00
(parallel nr.215)
Dejvice
NBFIT učebna
roomT9:302
Strachota P.
09:15–10:45
(lecture parallel1
parallel nr.103)

Dejvice
NBFIT učebna
roomT9:302
Kalvoda T.
11:00–12:30
(lecture parallel1
parallel nr.101)

Dejvice
NBFIT učebna
roomT9:301
Polívka O.
12:45–14:15
(parallel nr.104)
Dejvice
NBFIT učebna
roomT9:344
Polívka O.
14:30–16:00
(lecture parallel2
parallel nr.216)

Dejvice
NBFIT ucebna
Fri
roomT9:105
Pelantová E.
07:30–09:00
(lecture parallel1)
Dejvice
Posluchárna
roomT9:302
Milota J.
09:15–10:45
(lecture parallel2
parallel nr.211)

Dejvice
NBFIT učebna
roomT9:347
Petr I.
11:00–12:30
(lecture parallel2
parallel nr.202)

Dejvice
NBFIT učebna
roomT9:302
Petr I.
12:45–14:15
(lecture parallel2
parallel nr.205)

Dejvice
NBFIT učebna
roomT9:301
Čermáková D.
14:30–16:00
(lecture parallel1
parallel nr.107)

Dejvice
NBFIT učebna
roomT9:301
Čermáková D.
16:15–17:45
(lecture parallel2
parallel nr.206)

Dejvice
NBFIT učebna
roomT9:301
Čermáková D.
18:00–19:30
(lecture parallel1
parallel nr.114)

Dejvice
NBFIT učebna
roomT9:302
Marková K.
07:30–09:00
(lecture parallel2
parallel nr.203)

Dejvice
NBFIT učebna
roomT9:347
Marková K.
09:15–10:45
(lecture parallel2
parallel nr.212)

Dejvice
NBFIT učebna
roomT9:302
Milota J.
11:00–12:30
(lecture parallel2
parallel nr.204)

Dejvice
NBFIT učebna
Thu
roomT9:302
Kalvoda T.
07:30–09:00
(lecture parallel1
parallel nr.108)

Dejvice
NBFIT učebna
roomT9:301
Milota J.
09:15–10:45
(lecture parallel1
parallel nr.105)

Dejvice
NBFIT učebna
roomT9:346
Schmidt J.
11:00–12:30
(lecture parallel1
parallel nr.112)

Dejvice
NBFIT učebna
roomT9:301
Schmidt J.
12:45–14:15
(lecture parallel2
parallel nr.214)

Dejvice
NBFIT učebna
roomT9:301
Čermáková D.
14:30–16:00
(lecture parallel1
parallel nr.102)

Dejvice
NBFIT učebna
roomT9:301
Čermáková D.
16:15–17:45
(lecture parallel1
parallel nr.111)

Dejvice
NBFIT učebna
roomT9:301
Čermáková D.
18:00–19:30
(lecture parallel2
parallel nr.201)

Dejvice
NBFIT učebna
roomT9:105
Kalvoda T.
09:15–10:45
(lecture parallel2)
Dejvice
Posluchárna
roomT9:302
Milota J.
11:00–12:30
(lecture parallel1
parallel nr.113)

Dejvice
NBFIT učebna
roomT9:346
Řehořek T.
18:00–19:30
(parallel nr.217)
Dejvice
NBFIT učebna
Fri
roomT9:347
Bartoň T.
07:30–09:00
(lecture parallel1
parallel nr.115)

Dejvice
NBFIT učebna
roomT9:302
Petr I.
09:15–10:45
(lecture parallel1
parallel nr.109)

Dejvice
NBFIT učebna
roomT9:347
Petr I.
11:00–12:30
(lecture parallel1
parallel nr.106)

Dejvice
NBFIT učebna
roomT9:105
Pelantová E.
13:30–15:15
EVEN WEEK

(lecture parallel1)
Dejvice
Posluchárna
roomT9:347
Bartoň T.
09:15–10:45
(lecture parallel1
parallel nr.110)

Dejvice
NBFIT učebna
roomT9:105
Kalvoda T.
13:30–15:15
ODD WEEK

(lecture parallel2)
Dejvice
Posluchárna
Time-table for summer semester 2011/2012:
Time-table is not available yet
The course is a part of the following study plans:
Generated on 2012-7-9
For updated information see http://bilakniha.cvut.cz/en/predmet1122106.html