470-2101/04 – Principles of Mathematics (ZMA)
| Gurantor department | Department of Applied Mathematics | Credits | 2 |
| Subject guarantor | RNDr. Pavel Jahoda, Ph.D. | Subject version guarantor | RNDr. Pavel Jahoda, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | English |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | FEI | Intended for study types | Bachelor |
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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