|Course title||Mathematical Analysis 4|
|Organizational form of instruction||Lecture + Exercise|
|Level of course||Bachelor|
|Year of study||not specified|
|Number of ECTS credits||4|
|Language of instruction||Czech|
|Status of course||Compulsory|
|Form of instruction||Face-to-face|
|Work placements||This is not an internship|
|Recommended optional programme components||None|
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)
Understand differential and integral calculus of functions of several variables.
Comprehension Understand differential and integral calculus of functions of several variables.
Understanding the basic properties of functions of several variables.
KMA/MMAN3 and KAG/MA2
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|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.
|Study plans that include the course|