| Course Unit Code | 310-2110/01 |
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| Number of ECTS Credits Allocated | 2 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | First Cycle |
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| Year of Study * | First Year |
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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 | Czech |
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| Prerequisites and Co-Requisites | There are no prerequisites or co-requisites for this course unit |
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| Name of Lecturer(s) | Personal ID | Name |
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| JAH0037 | Mgr. Monika Jahodová, Ph.D. |
| Summary |
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Mathematics is essential part of education on technical universities.
It should be considered rather the method in the study of technical
courses than a goal. Thus the goal of mathematics is train logical
reasoning than mere list of mathematical notions, algorithms and
methods.
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| Learning Outcomes of the Course Unit |
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The set of real numbers, operations with algebraic expressions, equations and
inequalities, functions, exponential and logarithmic equations, trigonometric
functions and equations, analytic geometry, arithmetic and geometric sequences. |
| Course Contents |
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Week Syllabus of tutorial
-----------------------------------------------------------------------------1. Sets (integers, whole numbers, rational and irrational numbers, real numbers), intervals, operations on intervals (intersection, union, complement,…), neighbourhood of a point, absolute value.
2. Functions of one real variable (definition, domain, range, graph,…) Operations on functions (sum, difference, product, quotient), composite functions, properties of functions (even and odd functions, monotonic functions, bounded functions), one-to-one and inverse functions.
3. Elementary functions (linear, quadratic, rational and algebraic functions, exponential and logarithmic functions) and their properties. Drawing a sketch of the graph, graphs containing an absolute value.
4. Sine and Cosine functions, trigonometric functions. Definition by means of unit circle, values in radian measure, graphs, goniometric identities.
5. Test 1 (examining time: 20-30 minutes). Rational expressions: polynomials, fractions, exponents and roots.
6. Rational expressions: polynomials, fractions, exponents and roots.
7. Algebraic equations: linear equations (possibly with a parameter), quadratic equations (solutions in real numbers and in the complex plane), irrational equations.
8. Systems of two linear (and non-linear) equations in two unknowns. Linear inequalities (solutions by null point method), system of linear inequalities
9. The Exponential and logarithmic equations (inequalities respectively), properties of logarithms. Inverse functions.
10. Test 2 (examining time:20- 30 minutes). Domains of more complicated functions.
11. Analytic geometry in a geometric plane: point, vector, line (equations and a graph), circle (equations, determining its centre and radius).
12. The conic sections: the ellipse, the hyperbola (as a graph of a linear rational function), the parabola (as a graph of a quadratic function). Properties of conics.
13. Tangents to conic sections. Finding common points of a line and a conic. Test 3 (examining time: 20-30 minutes).
14. Reserve.
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| Recommended or Required Reading |
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| Required Reading: |
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[1] BIRD, J.: Engineering Mathematics, 4th ed. Newnes 2003.
[2] https://www.khanacademy.org/math/
Harshbarger, R.J. - Teynolds, J.J.: Calculus with Applications. D.C. Heath and Company, Lexington 1990, ISBN 0-669-21145-1 |
Polák, J.: Přehled středoškolské matematiky. SPN, Praha 1991. ISBN 80-7196-267-8
Polák, J.: Středoškolská matematika v úlohách I. Prometheus, Praha 1996. ISBN 80-7196-021-7
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| Recommended Reading: |
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| http://education-portal.com/academy/course/precalculus-course.html |
Středoškolské učebnice matematiky.
http://mdg.vsb.cz/portal/ |
| Planned learning activities and teaching methods |
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| Seminars, Tutorials, Other activities |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit | Credit | 100 (100) | 51 |
| Písemka | Written test | 100 | 51 |