| 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 | Face-to-face |
| Work placements | This is not an internship |
| Recommended optional programme components | None |
| Lecturer(s) |
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| Course content |
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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.
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| Learning activities and teaching methods |
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
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| Learning outcomes |
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Understand differential and integral calculus of multivariable functions.
Comprehension Understand differential and integral calculus of multivariable functions. |
| Prerequisites |
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Understanding the basic properties of multivariable functions and metric spaces.
KAG/MAN2 ----- or ----- KAG/MA2 and KMA/MAN3 |
| Assessment methods and criteria |
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Oral exam, Written exam
Credit: the student has to pass a written test (i.e. to obtain more than half of the possible points). 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 |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester | |
|---|---|---|---|---|
| Faculty: Faculty of Science | Study plan (Version): Mathematics for Education (2023) | Category: Mathematics courses | 2 | Recommended year of study:2, Recommended semester: Summer |