Course title  Mathematical Analysis 4 

Course code  KMA/MMAN4 
Organizational form of instruction  Lecture + Exercise 
Level of course  Bachelor 
Year of study  not specified 
Semester  Summer 
Number of ECTS credits  4 
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. Differential calculus in R^n: Partial derivatives and directional derivatives in R^n. Partial derivatives of higher order, interchanging the order of differentiation, total differential of a function and its application in approximate computing. Partial derivatives of compound functions. Differentials of higher order. The Taylor formula. Local extrema of functions, global extrema. 2. Implicit functions: Implicit functions of a single variable, its existence, uniqueness and differentiability. Extrema of implicit functions. Implicit functions of several variables. Constraint extrema, method of the Lagrange multipliers. 3. Integral calculus in R^n: The Jordan measure of a set in R^n. Properties of the measure. Definition and fundamental properties of the Riemann integral in R^n, its geometric interpretation. Multiple integration over intervals and normal domains. Substitution in integrals, especially polar, cylindrical and spherical coordinates. Practical aplications.

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

Learning outcomes 
Understand differential and integral calculus of functions of several variables.
Comprehension Understand differential and integral calculus of functions of several variables. 
Prerequisites 
Understanding the basic properties of functions of several variables.
KMA/MMAN3 and KAG/MA2  or  KMA/MA2M 
Assessment methods and criteria 
Oral exam, Written 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  Mathematics (1)  Mathematics courses  2  Summer 
Faculty of Science  Discrete Mathematics (2016)  Mathematics courses  2  Summer 