Course title  Mathematical Analysis 3 

Course code  KMA/MMAN3 
Organizational form of instruction  Lecture + Exercise 
Level of course  Bachelor 
Year of study  not specified 
Semester  Winter 
Number of ECTS credits  3 
Language of instruction  Czech 
Status of course  Compulsory 
Form of instruction  Facetoface 
Work placements  This is not an internship 
Recommended optional programme components  None 
Lecturer(s) 


Course content 
1. Sequences and series of functions: Pointwise and uniform convergence, convergence criteria (esp. the Weierstrass criterion). Properties of the limit function  limit, continuity, derivative and integral. 2. Power series: Radius, interval and domain of convergence. Uniform convergence of power series. Taylor series, Taylor expansion of elementary functions. Approximate computing via series. 3. Metric spaces: Metric on a set, examples of metric spaces. Normed linear space. Classification of points according to a set. Open and closed sets and their properties. Convergent and Cauchy sequences of points. 4. Functions and mappings in Euclid spaces: Practical aplications. Limit and continuity of a mapping (function). Properties of continuous functions on compact sets.

Learning activities and teaching methods 
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)

Learning outcomes 
Understand basic notions concerning function series and metric spaces.
Comprehension Understand basic notions concerning function series and metric spaces. 
Prerequisites 
Differential calculus of functions of several variables, integration on the real axis.
KAG/MA2  or  KAG/MMA2  or  KMA/MA2M 
Assessment methods and criteria 
Oral exam
Credit: the student has to pass two written tests (i.e. to obtain at least half of the possible points in each test). Attendance at seminars: absence is tolerated at most three times. Exam: the student has to understand the subject and be able to prove the principal results. 
Recommended literature 

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

Faculty of Science  Discrete Mathematics (2016)  Mathematics courses  2  Winter 
Faculty of Science  Mathematics (1)  Mathematics courses  2  Winter 