Course title  Calculus II 

Course code  UMB/565 
Organizational form of instruction  Lecture + Lesson 
Level of course  Bachelor 
Year of study  not specified 
Frequency of the course  In each academic year, in the summer semester. 
Semester  Summer 
Number of ECTS credits  8 
Language of instruction  Czech 
Status of course  Compulsory 
Form of instruction  unspecified 
Work placements  unspecified 
Recommended optional programme components  None 
Lecturer(s) 


Course content 
Content of lectures: 1. Sequences: definition, examples, basic concepts, convergence, absolute and relative convergence, theorems on sequences, definition of limsup and liminf of sequences, arithmetic and geometric sequences 2. Infinite series: sum of a series, BolzanoCauchy condition on series convergence, properties of series, criteria for convergence of series, absolute convergence 3. Functional sequences and series: point and uniform convergence, example of functional sequence with point convergence but not with uniform convergence, Weierstrass criterion of uniform convergence, properties of uniformly convergent sequences and series 4. Power series: range of convergence of power series and its determination, basic properties of power series, Taylor series 5. Indefinite integral: definition, basic properties, substitution method, integration by parts, methods of integration of rational, trignometric and irrational functions 6. Riemann (definite) integral: definition, basic concepts, existence, substitution method and integration by parts for Riemann integral, relationship between indefinite and Riemann integral (Newton formula) 7. Improper integral: definition, convergence, integral criterion for convergence of infinite series 8. Geometric application of Riemann integral: mean value of function, derivation of formulae for area between two curves, surfaces and volumes of solids of revolution, and length of curves Content of practicals: Practicing theoretical concepts on specific examples.

Learning activities and teaching methods 
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Demonstration, Projection

Learning outcomes 
Introduction to series and single variable integration.
Student should be able to explain what are sequences of numbers and infinite series and also why a sum of infinite amount of numbers can be a finite number. Student should also know how to calculate limits of sequences and whether a given infinite series converges or not. Last but not least, student should understand meaning of integration of functions, why is it needed and which practical applications integration has. (S)he should also know how to define Riemann integral and how to work with it. 
Prerequisites 
Students are assumed to have knowledge of calculus covered by the courses Matematická analýza I (UMB564).
UMB/010  or  UMB/551  or  UMB/564 
Assessment methods and criteria 
Combined exam, Test, Interim evaluation
100% attendance of practicals (excused absence permitted), performance of all written tests on practicals and at least 50% success in these tests 
Recommended literature 

Study plans that include the course 
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