714-0066/02 – Bachelor Mathematics I (BMI)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 5 |
| Subject guarantor | doc. RNDr. Jarmila Doležalová, CSc. | Subject version guarantor | doc. RNDr. Jarmila Doležalová, CSc. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | | Semester | winter |
| | Study language | Czech |
| Year of introduction | 1999/2000 | Year of cancellation | 2009/2010 |
| Intended for the faculties | FBI | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
This course is closed.
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.
This course is closed.
Teaching methods
Individual consultations
Tutorials
Other activities
Summary
The functions of one real variable, the derivation of a
function of one variable. Derivations of higher orders. Investigating the
behaviour of functions. Antiderivative and the indefinite integral, some
properties, elementary methods of integration. Linear algebra: Arithmetic
vectors, matrices, determinants, systems of linear algebraic equations.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
E-learning
Other requirements
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Funkce jedné reálné proměnné
Definiční obor, obor hodnot, funkce sudá, lichá, periodická, ohraničená,
neohraničená, monotonní, složená, prostá, inverzní. Elementární funkce. Limita
funkce, spojitost funkce.
Derivace funkce jedné proměnné
Definice, geometrický a fyzikální význam. Vzorce a pravidla pro derivování.
Derivace vyšších řádů. Diferenciál funkce. L´Hospitalovo pravidlo monotonnost,
lokální extrémy, konvexnost, konkávnost, inflexní body, asymptoty. Derivace
parametricky zadané funkce.
Lineární algebra
Aritmetické vektory, operace, lineární závislost a nezávislost. Matice, hodnost
matice, operace s maticemi. Typy matic - regulární, jednotková, inverzní.
Determinanty, definice, vlastnosti, výpočet hodnoty. Soustavy lineárních
algebraických rovnic, Cramerovo pravidlo, Frobeniova věta, Gaussova eliminační
metoda.
Analytická geometrie v prostoru
Geometrické vektory, operace s nimi. Skalární, vektorový, smíšený součin a
jejich užití. Analytické vyjádření roviny a přímky v prostoru, jejich vzájemné
poloha, metrické úlohy.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.