470-2101/03 – Principles of Mathematics (ZMA)

Gurantor departmentDepartment of Applied MathematicsCredits2
Subject guarantorRNDr. Pavel Jahoda, Ph.D.Subject version guarantorRNDr. Pavel Jahoda, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFEIIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
JAH02 RNDr. Pavel Jahoda, Ph.D.
LIT40 Ing. Martina Litschmannová, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit 0+2
Part-time Credit 0+10

Subject aims expressed by acquired skills and competences

Student gets the bysic knowledges and skills which are neresary for further studies at VSB-TUO during the course. Students are able to evaluate the truth value of the logical statement, explain the difference between the basic numeric sets, edit the algebraic expression to describe the properties of functions, their domains, to quantify the functional values of elementary functions in the notable points and draw the graphs of these functions. In addition, the student is able to solve linear, quadratic, exponential, logarithmic and trigonometric equations and inequalities and to use this skills to solve elementary problems of analytic geometry.

Teaching methods

Tutorials

Summary

Precalculus is an advanced form of secondary school algebra. Precalculus are intended to prepare students for the study of calculus and includes a review of algebra and trigonometry, as well as an introduction to exponential, logarithmic and trigonometric functions, vectors, complex numbers and analytic geometry.

Compulsory literature:

R. G. Brown, D. P. Robbins: Advanced Mathematics (A Precalculus Course), Houghton Mifflin Comp., Boston 1989. Libor Šindel: Principles of mathematics (The text is in electronic form).

Recommended literature:

Richard G. Brown, David P. Robbins, Advanced Mathematics a precalculus course

Way of continuous check of knowledge in the course of semester

Students will be continuously addressed examples to practice. A condition for granting credit is an active participation in seminars and passing the final test.

E-learning

Other requirements

Students will be continuously addressed examples to practice. A condition for granting credit is an active participation in seminars and passing the final test.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Syllabus of lectures: - Sets. Mathematical induction. - Rational numbes. Which numbers have rational square roots? What is a real number? Complex numbers. - The formal rules of algebra. Completing the square. Solving a quadratic equation by completing the square. The quadratic formula. Synthetic division by x − a. The fundamental theorem of algebra. - Functions. What is a function? Functional notation. A function of a function. The graph of a function. Coördinate pairs of a function. Odd and even functions. - Basic graphs. The constant function. The identity function. The absolute value function. A parabola. The square root function. The cubic function. Translations of a graph. - Linear functions. The graph of a first degree equation -- a straight line. Polynomials of the second degree. Solving a quadratic equation by factoring. A double root. Quadratic inequalities. The sum and product of the roots. - Polynomial functions. Definition of a polynomial in x. The degree of a term and of a polynomial. The leading coefficient. The general form of a polynomial. The roots, or zeros, of a polynomial. The polynomial equation. The roots of a polynomial. - The slope of a straight line. Definition of the slope. Positive and negative slope. A straight line has only one slope. Perpendicular lines. - Rational functions. - Inverse functions. Definition of inverses. Constructing the inverse. The graph of an inverse function. - Logarithmic and exponential functions. Logarithms.The system of common logarithms. The system of natural logarithms. The three laws of logarithms. Change of base. - Trigonometric functions. - Analytic geometry.

Conditions for subject completion

Part-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit Credit 30  10
Mandatory attendence parzicipation: Active participation in the 80% of the exercises is mandatory.

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2020/2021 (B0541A170008) Computational and Applied Mathematics P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0541A170008) Computational and Applied Mathematics K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0541A170008) Computational and Applied Mathematics P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0541A170008) Computational and Applied Mathematics K Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

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