714-0365/03 – Basics of Mathematics (ZM)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 2 |
| Subject guarantor | Mgr. Milena Luňáčková, Ph.D. | Subject version guarantor | Mgr. Milena Luňáčková, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2007/2008 | Year of cancellation | 2012/2013 |
| Intended for the faculties | FS | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
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.
Students should learn how to
analyze problems,
distinguish between important and unimportant,
suggest a method of solution,
verify each step of a method,
generalize achieved results,
analyze correctness of achieved results with respect to given conditions,
apply these methods while solving technical problems,
understand that mathematical methods and theoretical advancements
outreach the field mathematics.
Teaching methods
Seminars
Other activities
Summary
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.
Compulsory literature:
Recommended literature:
http://education-portal.com/academy/course/precalculus-course.html
Additional study materials
Way of continuous check of knowledge in the course of semester
Klasifikovaný zápočet je hodnocen známkou jako u zkoušky. Body získá student :
1. 0-10 bodů za docházku a aktivitu ve cvičení
2. 0-90 bodů za písemky, viz osnova. V každé budou 3 příklady po 10 bodech.
E-learning
http://mdg.vsb.cz/M/
http://www.studopory.vsb.cz/materialy.html
Other requirements
there are no additional requirements
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Week Syllabus of tutorial
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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: 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: 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: 30 minutes).
14. Reserve.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction