Elemnts of calculus
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 Tue Fri Thu Fri - Time-table for summer semester 2011/2012:
- Time-table is not available yet
- The course is a part of the following study plans:
-
- Computer Science, Version for Students who Enrolled in 2009 and 2010, Presented in Czech (compulsory course in the program)
- Computer engineering, Version for Students who Enrolled in 2009 and 2010, in Czech (compulsory course in the program)
- 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)
- Information Technology, Version for Students who Enrolled in 2009 and 2010, Presented 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 2011 and 2012 (in Czech) (compulsory course in the program)
- Information Systems and Management - Version for those who Enrolled in 2011 and 2012 (in Czech) (compulsory course in the program)
- Information Technology- Version for those who Enrolled in 2011 and 2012 (in Czech) (compulsory course in the program)
- Computer Engineering, Version for those who Enrolled in 2011 and 2012, in Czech (compulsory course in the program)
- Software Engineering- Version for those who Enrolled in 2011 and 2012 (in Czech) (compulsory course in the program)
- Computer Science - Version for those who Enrolled in 2011 and 2012 (in Czech) (compulsory course in the program)
- Web and Multimedia- Version for those who Enrolled in 2011 and 2012 (in Czech) (compulsory course in the program)