| Course title | Calculus I |
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| Course code | UMB/564I |
| Organizational form of instruction | Lecture + Lesson |
| Level of course | Bachelor |
| Year of study | 1 |
| Frequency of the course | In each academic year, in the winter semester. |
| Semester | Winter |
| Number of ECTS credits | 6 |
| Language of instruction | English |
| 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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Content of lectures: 1. Review (Functions, Inverse Functions, Trig Functions, Exponential Functions, Logarithm Functions, Common Graphs) 2. Limits (One-sided limits, Tangent Lines and Rates of Change, Limit Properties, Computing Limits, Limits Involving Infinity) 3. Continuity (Definition, One-sided limits, Upper and Lower Bound Theorem, Mean Value Theorem) 4. Derivatives (Definition, Interpretation of the Derivative, Non-differentiable functions) 5. Differentiation Formulas (Product and Quotient Rule, Derivatives of Trig Functions, Derivatives of Exponential and Logarithm Functions, Derivatives of Inverse Trig Functions Derivatives of Hyperbolic Trig Functions, Chain Rule, Implicit Differentiation, Higher Order Derivatives) 6. Applications of Derivatives (Critical Points, Minimum and Maximum Values, Increasing and Decreasing Functions, Inflection points, Concavity, the Second Derivative Test) 7. Mean Value Theorem, Optimization Problems, L'Hospital's Rule and Indeterminate Forms, Linear Approximations, Differentials, Newton's Method 8. Taylor series Content of practicals: Functions, limits and derivatives. Various applications.
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| Learning activities and teaching methods |
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming)
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| Learning outcomes |
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To develop basic concepts of differential calculus.
Learning the basics of differential calculus. |
| Prerequisites |
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Basic knowledge of mathematics from a secondary school is expected.
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| Assessment methods and criteria |
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Oral examination, Student performance assessment, Test
1. a regular attendance - up to 4 missed tutorials will be tolerated 2. a successful elaboration of 5 homeworks (with at least 50% of content), homeworks will be checked during the oral exam. |
| 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): Bioinformatics (1) | Category: Informatics courses | 1 | Recommended year of study:1, Recommended semester: Winter |