| Course Unit Code | 714-0866/01 |
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| Number of ECTS Credits Allocated | 5 ECTS credits |
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| Type of Course Unit * | Optional |
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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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| BEL10 | Mgr. Jana Bělohlávková |
| ZID76 | Mgr. Arnošt Žídek, Ph.D. |
| KOT31 | RNDr. Jan Kotůlek, Ph.D. |
| Summary |
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Course description
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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Goals
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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Program of lectures
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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.
Program of exercises and seminars:
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1 Basic operations with matrices. Determinants. Calculation of determinant developing the elements of any series.
2 Rank of matrix, inverse matrix.
3 Solution of linear equations.
4 Solution of systems of linear equations.
5 1. test (calculate determinant, rank of matrix, solution of the system, the inverse matrix).
6 Functions of a simple, inverse, compound. Elementary functions. Trigonometric functions.
7 2.test (domain, inverse function). Limits of functions.
8 Differentiation of functions.
9 Derivations and differential, equations of tangents and normals point functions.
10 Calculation of the limit L'Hospital rule functions. Extremes of function.
11 Convex and concave function, inflection point.
12 3.test (derivative of the function, use). Asymptotes of the curve. A function.
13 Analytic geometry.
14 Reserve and credits.
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| 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.
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| Recommended 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.
|
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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| 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 |