Elements of Calculus

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:

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 učebnaroomT9:301 Kalvoda T. 11:00–12:30 (lecture parallel1 parallel nr.102) Dejvice NBFIT učebnaroomT9:301 Kalvoda T. 12:45–14:15 (lecture parallel1 parallel nr.103) Dejvice NBFIT učebnaroomTH: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 učebnaroomT9:301 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 učebnaroomTH: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 učebnaroomTH: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 učebnaroomT9:302 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 PosluchárnaroomTH: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 PosluchárnaroomT9:155 Kalvoda T. 16:15–17:45 EVEN WEEK (lecture parallel2) Dejvice PosluchárnaroomT9:347 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 učebnaroomTH: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 PosluchárnaroomTH: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 učebnaroomTH: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 učebnaroomT9:347 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:

Software Engineering, Version for Students who Enrolled in 2009 and 2010, in Czech (compulsory course in the program)
Web and Multimediac, Version for Students who Enrolled in 2009 and 2010, Presented in Czech (compulsory course in the program)
Information Systems and Management, Version for Students who Enrolled in 2009 and 2010, in Czech (compulsory course in the program)
Informatics, Version for Students who Enrolled in 2009 and 2010, Presented in Czech (compulsory course in the program)
Informatics (Bachelor)- Version for those who Enrolled in 1 and 2012 (in Czech) (compulsory course in the program)
Information Systems and Management - Version for those who Enrolled in 2011 (in Czech) (compulsory course in the program)
Information Technology - Version for those who Enrolled in 2011 (in Czech) (compulsory course in the program)
Computer Engineering, Version for those who Enrolled in 2011, in Czech (compulsory course in the program)
Software Engineering- Version for those who Enrolled in 2011 (in Czech) (compulsory course in the program)
Computer Science - Version for those who Enrolled in 2011 (in Czech) (compulsory course in the program)
Web and Multimedia- Version for those who Enrolled in 2012 (in Czech) (compulsory course in the program)
Informatics (Bachelor) - Version for those who Enrolled in 2011 (in Czech) (compulsory course in the program)
Web and Multimedia- Version for those who Enrolled in 2011 (in Czech) (compulsory course in the program)
Computer Science - Version for those who Enrolled in 2012 (in Czech) (compulsory course in the program)
Information Technology - Version for those who Enrolled in 2012 (in Czech) (compulsory course in the program)
Computer Engineering, Version for those who Enrolled in 2012, in Czech (compulsory course in the program)
Software Engineering- Version for those who Enrolled in 2012 (in Czech) (compulsory course in the program)
Information Systems and Management - Version for those who Enrolled in 2012 (in Czech) (compulsory course in the program)
Informatics (Bachelor)- Version for those who Enrolled in 2013 (in Czech) (compulsory course in the program)
Web and Multimedia- Version for those who Enrolled in 2013 (in Czech) (compulsory course in the program)
Computer Science - Version for those who Enrolled in 2013 (in Czech) (compulsory course in the program)
Information Technology - Version for those who Enrolled in 2013 (in Czech) (compulsory course in the program)
Computer Engineering, Version for those who Enrolled in 2013, in Czech (compulsory course in the program)
Software Engineering- Version for those who Enrolled in 2013 (in Czech) (compulsory course in the program)
Information Systems and Management - Version for those who Enrolled in 2013 (in Czech) (compulsory course in the program)
Informatics (Bachelor)- Version for those who Enrolled in 2014 (in Czech) (compulsory course in the program)
Web and Multimedia- Version for those who Enrolled in 2014 (in Czech) (compulsory course in the program)
Computer Science - Version for those who Enrolled in 2014 (in Czech) (compulsory course in the program)
Information Technology - Version for those who Enrolled in 2014 (in Czech) (compulsory course in the program)
Computer Engineering, Version for those who Enrolled in 2014, in Czech (compulsory course in the program)
Software Engineering- Version for those who Enrolled in 2014 (in Czech) (compulsory course in the program)
Information Systems and Management - Version for those who Enrolled in 2014 (in Czech) (compulsory course in the program)
Bc. Programme Informatics, in Czech, Version 2015 and 2016 (compulsory course in the program)
Bc. Branch Security and Information Technology, in Czech, Version 2015, 2016 and 2017 (compulsory course in the program)
Bc. Branch Computer Science, in Czech, Version 2015, 2016 and 2017 (compulsory course in the program)
Bc. Branch Computer Engineering, Version 2015, 2016 and 2017, in Czech (compulsory course in the program)
Bachelor Branch Information Systems and Management, in Czech, Version 2015 and 2016 (compulsory course in the program)
Bachelor Branch Knowledge Engineering, in Czech, Version 2015 and 2016 (compulsory course in the program)
Bachelor Branch WSI, Specialization Software Engineering, in Czech, Version 2015 and 2016 (compulsory course in the program)
Bachelor Branch, Specialization Web Engineering, in Czech, Version 2015 and 2016 (compulsory course in the program)
Bachelor Branch WSI, Specialization Computer Grafics, in Czech, Version 2015 and 2016 (compulsory course in the program)