| Course title | Calculus I |
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| Course code | UMB/564 |
| Organizational form of instruction | Lecture + Lesson |
| Level of course | Bachelor |
| 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 | Compulsory, Compulsory-optional |
| 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 3. Sets, supremum, infimum, Euler number 4. Functions, operations, inverse function 5. Review of elementary functions, powers, power function, operations with functions, trigonometric functions 6. Limits: One-sided limits, Tangent Lines and Rates of Change, Limit Properties, Computing Limits, Limits Involving Infinity 7. Operations with limits, squeeze theorem and applications 8. Continuity: Definition, One-sided continuity, Upper and Lower Bound Theorem, Bolzano theorem 9. Operations with continuous functions, maximum and minimum 10. Derivatives: Definition, Interpretation of the Derivative, Differential 11. Differentiation Formulas: Product and Quotient Rule, Derivatives of elementary functions, Chain Rule, Implicit Differentiation, Higher Order Derivatives 12. Applications of Derivatives: Critical Points, Minimum and Maximum Values, Increasing and Decreasing Functions, Inflection points, Concavity, the Second Derivative Test) 13. Mean Value Theorem, Optimization Problems, L'Hopital'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, Combined exam, Interim evaluation
1. Continuous study throughout the semester. 2. Regular attendance at labs. 2. Score at least 50% from lab tests written during the course. 3. Score at least 50% from lab homeworks. |
| 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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