Course title  Calculus III for Combined Studies 

Course code  UMB/566K 
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 winter semester. 
Semester  Winter 
Number of ECTS credits  8 
Language of instruction  Czech 
Status of course  unspecified 
Form of instruction  Facetoface 
Work placements  This is not an internship 
Recommended optional programme components  None 
Lecturer(s) 


Course content 
Content of lectures: 1. Infinite Series, convergence/divergence, absolute convergence of series. 2. Criteria for convergence of series  ratio test, root test. 3. Sequences and series functions  fundamental notions. 4. Criteria for convergence of series, uniform convergence. 5. Power series (Power series and functions, Maclaurin and Taylor series, Applications of series, Binomial series) 6. Fourier series. 7. Vector functions of multiple variables (continuity, limits, derivatives, gradient, total differential, Jacobian matrix) 8. Vector functions (parametric equations of curves, calculus with vector functions, arc length, tangent and normal vectors, velocity and acceleration, curvature) 9. Multiple integrals (double and triple integrals, Fubini's theorem, integrals in polar, cylindrical and spherical coordinates, change of variables, area and volume). 10. Curve integrals of 1st and 2nd type (in a scalar and in a vector fields).

Learning activities and teaching methods 
Monologic (reading, lecture, briefing), Individual preparation for exam

Learning outcomes 
To develop differential and integral calculus of functions of several variables.
We will work with sequences and series of numbers and functions. We learn how to decide about their convergence. We will expand functions into Taylor and Fourier series and show their connection to the original functions frow which the series were derived. We show how to calculate double and curve integrals. 
Prerequisites 
We assume knowledge of differentail calculus of one and more variables and of integral calculus of one real variable (e.g. UMB/010K a UMB/565K).
UMB/565  or  UMB/565K 
Assessment methods and criteria 
Written examination
Simple written homeworks. Written exam. To pass the exam it is necessary to reach at least 50% points. 
Recommended literature 

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