| Course Unit Code | 310-2301/01 |
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| Number of ECTS Credits Allocated | 5 ECTS credits |
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| Type of Course Unit * | Choice-compulsory |
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| Level of Course Unit * | First Cycle |
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| Year of Study * | |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | English |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| KOT31 | RNDr. Jan Kotůlek, Ph.D. |
| Summary |
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I. Calculus.
Function of one variable (basic notions, inverse function, elementary functions);
Limits and Continuity of a function;
Differentiation of a function (differentiation rules, application, L'Hospital's rule).
II. Linear algebra.
Vector spaces;
Matrices and determinants;
Systems of linear algebraic equations (Gaussian elimination, Frobeniu theorem).
III. Introduction to analytic geometry (lines and planes in E3, intersection, distance, angle).
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| Learning Outcomes of the Course Unit |
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After completing this course, students should have the following skills:
* Use rules of differentiation to differentiate functions.
* Sketch the graph of a function using asymptotes, critical points.
* Apply differentiation to solve problems.
* Solve a system of linear algebraic equations.
* Work with basic objects in three dimensional Euclidean space. |
| Course Contents |
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1 Linear algebra. Operations with matrices. Determinants. Properties of determinants.
2 Rank of a matrix. Inverse matrix.
3 Solution of linear equations. Frobenius theorem. Cramer's rule.
4 Gaussian elimination algorithm.
5 Real functions of one real variable. Definitions, graph. Function bounded, monotonous,
even, odd, periodic. One-to-one function, inverse and composite functions.
6 Elementary functions.
7 Limit of a function. Continuous and discontinuous functions.
8 Differential calculus of one variable. Derivative of a function, its geometrical and
physical applications. Rules of differentiation.
9 Derivatives of elementary functions.
10 Differential functions. Derivative of a function defined parametrically. Derivatives of
higher orders. L'Hospital's rule.
11 Use of derivatives to detect monotonicity, convexity and concavity features.
12 Extrema of functions. Asymptotes. Graph of a function.
13 Analytic geometry in E3. Scalar, cross and triple product of vectors and their properties.
14 Equation of a line. Equation of a plane. Relative positions problems.
Metric or distance problems. |
| Recommended or Required Reading |
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| Required Reading: |
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Neustupa J.: Mathematics I. ČVUT, Praha 2004.
Demlova M., Hamhalter J.: Calculus I. ČVUT, Praha 1998, ISBN 80-01-01110-0.
Doležalová, J., Mathematics I. VŠB-TU Ostrava 2005, ISBN 80-248-0796-3.
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Neustupa J.: Mathematics I. ČVUT, Praha 2004.
Demlova M., Hamhalter J.: Calculus I. ČVUT, Praha 1998, ISBN 80-01-01110-0.
Doležalová, J., Mathematics I. VŠB-TU Ostrava 2005, ISBN 80-248-0796-3.
|
| Recommended Reading: |
|---|
Neustupa J.: Mathematics I. ČVUT, Praha 2004.
Demlova M., Hamhalter J.: Calculus I. ČVUT, Praha 1998, ISBN 80-01-01110-0
Doležalová, J., Mathematics I. VŠB-TU Ostrava 2005, ISBN 80-248-0796-3.
|
Neustupa J.: Mathematics I. ČVUT, Praha 2004.
Demlova M., Hamhalter J.: Calculus I. ČVUT, Praha 1998, ISBN 80-01-01110-0
Doležalová, J., Mathematics I. VŠB-TU Ostrava 2005, ISBN 80-248-0796-3.
|
| Planned learning activities and teaching methods |
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| Lectures, Individual consultations, Tutorials |
| Assesment methods and criteria |
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| Tasks are not Defined |