### Course: Mathematical Analysis II

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 Course title Mathematical Analysis II KMA/7MA2 Lecture + Seminary Bachelor not specified Winter 4 Czech Compulsory Face-to-face This is not an internship None
Lecturer(s)
• Petrášková Vladimíra, doc. RNDr. Ph.D.
Course content
1. Function limit (definition). Limits of functions created by arithmetic operations. Limits of a compound function. Inequality theorems. 2. Continuity of a function at a point, on an interval. 3. Theorem on the limit of a monotone function. Properties of continuous functions. 4. Derivation of a function in a point. Derivation theorems - arithmetic operations, compound function. 5. Calculation of derivatives from a) definition, b) based on formulas. 6. Higher order derivatives. L'Hospital's rule. 7. Monotonicity of a function in a point. Absolute extreme of a function on a set (interval). Monotonicity of a function in an interval. 8. Local extreme of a function, necessary and sufficient condition, calculation of derivation. 9. Convexity and concavity of a function in an interval. 10. Convex, concave point function. Inflection point. Asymptote function. 11. Investigation of the course of the function. 12. - 14. Different meanings of derivation in applications (word problems).

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book)
Learning outcomes
The aim of the course is to acquaint students with the basics of differential calculus of one variable.
The student will gain the knowledge and skills needed to master the problems of differential equations, number series and the basics of probability and statistics.
Prerequisites
unspecified

Assessment methods and criteria
Student performance assessment, Combined exam

During the semester, completion of two written tests and elaboration of assigned tasks. Passing the written final test.
Recommended literature
• Petrášková, Vladimíra; Štěpánková, Hana. Algebraické funkce a diferenciální počet funkcí jedné proměnné. 1. vyd. České Budějovice : Jihočeská univerzita, 2014. ISBN 978-80-7394-473-5.
• Petrášková, Vladimíra; Zmeškalová, Eva. Algebraické funkce. 1. vyd. České Budějovice : Jihočeská univerzita v Českých Budějovicích, 2005. ISBN 80-7040-825-1.
• Samková, L. Sbírka příkladů z matematiky. ČVUT, Praha, 2006.

 Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester