CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2018/2019

Elements of Calculus

Code Completion Credits Range Language
BI-ZMA Z,ZK 6 3P+2C 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:
Further information:
https://courses.fit.cvut.cz/BI-ZMA/
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 roomT9:301Zhouf J.11:00–12:30(parallel nr.208)DejviceNBFIT učebnaroomT9:105Kalvoda T.14:30–16:00EVEN WEEK(lecture parallel1)DejvicePosluchárnaroomT9:301Zhouf J.16:15–17:45(parallel nr.101)DejviceNBFIT učebnaroomT9:301Zhouf J.18:00–19:30(parallel nr.102)DejviceNBFIT učebna roomTK:BSHrabáková J.11:00–12:30ODD WEEK(lecture parallel3)DejviceNTK Ballingův sálroomTH:A-1442Zhouf J.12:45–14:15(parallel nr.108)Thákurova 7 (FSv-budova A)roomT9:105Petr I.14:30–16:00ODD WEEK(lecture parallel2)DejvicePosluchárnaroomT9:302Kalvoda T.16:15–17:45(parallel nr.301)DejviceNBFIT učebnaroomT9:346Hrabáková J.18:00–19:30(parallel nr.302)DejviceNBFIT učebna roomT9:302Petr I.12:45–14:15(parallel nr.303)DejviceNBFIT učebnaroomTK:BSHrabáková J.14:30–16:00(lecture parallel3)DejviceNTK Ballingův sál roomT9:346Mazáč J.07:30–09:00(parallel nr.103)DejviceNBFIT učebnaroomT9:346Mazáč J.09:15–10:45(parallel nr.104)DejviceNBFIT učebnaroomTH:A-1342Zhouf J.11:00–12:30(parallel nr.105)Thákurova 7 (FSv-budova A)roomT9:302Čermáková D.16:15–17:45(parallel nr.106)DejviceNBFIT učebnaroomT9:302Čermáková D.18:00–19:30(parallel nr.107)DejviceNBFIT učebna roomTH:A-1442Jureček M.09:15–10:45(parallel nr.304)Thákurova 7 (FSv-budova A)roomTH:A-1442Olšák P.16:15–17:45(parallel nr.109)Thákurova 7 (FSv-budova A)roomTH:A-1442Olšák P.18:00–19:30(parallel nr.110)Thákurova 7 (FSv-budova A) roomTH:A-1442Jureček M.11:00–12:30(parallel nr.305)Thákurova 7 (FSv-budova A)roomT9:302Čermáková D.14:30–16:00(parallel nr.213)DejviceNBFIT učebna roomTH:A-1242Petr I.12:45–14:15(parallel nr.306)Thákurova 7 (FSv-budova A) roomT9:105Petr I.07:30–09:00(lecture parallel2)DejvicePosluchárnaroomT9:346Petr I.09:15–10:45(parallel nr.201)DejviceNBFIT učebnaroomT9:302Tichý J.14:30–16:00(parallel nr.202)DejviceNBFIT učebnaroomTH:A-1342Strmisková L.16:15–17:45(parallel nr.203)Thákurova 7 (FSv-budova A)roomTH:A-1342Strmisková L.18:00–19:30(parallel nr.204)Thákurova 7 (FSv-budova A) roomT9:346Tichý J.07:30–09:00(parallel nr.207)DejviceNBFIT učebna roomT9:347Kalvoda T.11:00–12:30(parallel nr.307)DejviceNBFIT učebnaroomT9:105Kalvoda T.14:30–16:00(lecture parallel1)DejvicePosluchárnaroomT9:347Hrabák P.18:00–19:30(parallel nr.212)DejviceNBFIT učebna roomTH:A-1442Štampach F.12:45–14:15(parallel nr.206)Thákurova 7 (FSv-budova A)roomT9:347Hrabák P.14:30–16:00(parallel nr.205)DejviceNBFIT učebnaroomT9:347Hrabák P.16:15–17:45(parallel nr.310)DejviceNBFIT učebna roomT9:347Kalvoda T.12:45–14:15(parallel nr.308)DejviceNBFIT učebnaroomTH:A-1442Štampach F.14:30–16:00(parallel nr.309)Thákurova 7 (FSv-budova A) roomT9:302Olšák P.07:30–09:00(parallel nr.209)DejviceNBFIT učebnaroomTH:A-1242Pauš P.09:15–10:45(parallel nr.111)Thákurova 7 (FSv-budova A)roomTH:A-1242Pauš P.11:00–12:30(parallel nr.112)Thákurova 7 (FSv-budova A)roomT9:346Olšák P.12:45–14:15(parallel nr.113)DejviceNBFIT učebna roomT9:302Olšák P.09:15–10:45(parallel nr.210)DejviceNBFIT učebnaroomTH:A-1242Pauš 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 2019-05-23
For updated information see http://bilakniha.cvut.cz/en/predmet1122106.html