| Course title | Calculus I |
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| Course code | UMB/CV564 |
| Organizational form of instruction | Lecture + Lesson |
| Level of course | unspecified |
| Year of study | not specified |
| Frequency of the course | In each academic year, in the winter semester. |
| Semester | Winter |
| Number of ECTS credits | 6 |
| Language of instruction | Czech |
| Status of course | unspecified |
| Form of instruction | unspecified |
| Work placements | unspecified |
| Recommended optional programme components | None |
| Lecturer(s) |
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| Course content |
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1. Numbers: Natural numbers, Peano axioms, rational numbers, real and complex numbers 2. Mappings: countable and uncountable sets, supremum and infimum 3. Functions: Review of elementary functions, powers, power function, operations with functions, inverse functions, inverse trigonometric functions 4. Limits: One-sided limits, Tangent Lines and Rates of Change, Limit Properties, Computing Limits, Limits Involving Infinity 5. Continuity: Definition, One-sided continuity, Upper and Lower Bound Theorem, Bolzano theorem 6. Derivatives: Definition, Interpretation of the Derivative, Differential 7. Differentiation Formulas: Product and Quotient Rule, Derivatives of elementary functions, Chain Rule, Implicit Differentiation, Higher Order Derivatives 8. Applications of Derivatives: Critical Points, Minimum and Maximum Values, Increasing and Decreasing Functions, Inflection points, Concavity, the Second Derivative Test) 9. Mean Value Theorem, Optimization Problems, L'Hospital's Rule and Indeterminate Forms, Linear Approximations, Newton's Method
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| Learning activities and teaching methods |
Monologic (reading, lecture, briefing)
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| Learning outcomes |
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To develop basic concepts of differential calculus.
Students will learn basics of differential calculus of single variable. |
| Prerequisites |
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Level at the state high school exam in mathematics is expected.
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| Assessment methods and criteria |
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Student performance assessment
1. Regular attendance during lectures and labs 2. Score at least 50% from tests written during the course 3. Score at least 50% from final exam |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester |
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