230-0308/01 – Mathematics II (MII)
| Gurantor department | Department of Mathematics | Credits | 5 |
| Subject guarantor | Ing. Lukáš Pospíšil, Ph.D. | Subject version guarantor | Ing. Lukáš Pospíšil, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | summer |
| | Study language | English |
| Year of introduction | 2021/2022 | Year of cancellation | |
| Intended for the faculties | FBI | 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 matematics.
Teaching methods
Lectures
Individual consultations
Tutorials
Summary
Indefinite integral, some properties, elementary methods of integration. The
differential calculus of functions of two variables,the partial derivations,
extremes of functions of two variables. Ordinary differential equations,first
order differential equations, types of solution, separable, homogenous and
linear equations. Linear equations of the 2nd order with constant coefficients.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
Za testy může získat student 5 - 15 bodů.
(Student, který získá zápočet, bude hodnocen 10 - 20 bodů).
Podmínky pro udělení zápočtu (kombinované studium):
Za účast na konzultacích může student získat 5 - 20 bodů, v případě neúčasti může student získat 5 bodů za zpracování zadaného programu.
Požadavky ke zkoušce:
Podmínkou pro účast na zkoušce je zapsaný zápočet z příslušného předmětu.
Písemná část zkoušky bude hodnocena 0 - 60 body, za její úspěšné absolvování bude považován zisk 25 bodů.
Ústní část zkoušky bude hodnocena 0 - 20 body, za její úspěšné absolvování bude považován zisk 5 bodů.
Po sečtení bodů získaných za zápočet, písemnou a ústní část zkoušky bude student hodnocen výborně, velmi dobře, dobře a nevyhověl, podle tabulky studijního a zkušebního řádu VŠB - TUO.
Pro zapsání zkoušky podle tabulky musí student úspěšně absolvovat obě části kombinované zkoušky a dosáhnout potřebného počtu bodů.
Bodové hodnocení:
86 - 100 výborně
66 - 85 velmi dobře
51 - 65 dobře
0 - 50 nevyhověl
E-learning
www.studopory.vsb.cz
mdg.vsb.cz
Other requirements
No more requirements are put on the student.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Integrational calculus of function of one veriable. Primitive function and undefinite integral. Integration of elementary functions.
2. Basic integrational methods - per partes and substitution.
3. Integration of rational functions.
4. Integration of goniometric functions and irational functions.
5. Definite integral: basic terms, their properties, Newton-Leibniz theorem. Geometrical meaning of definite integral. Substitution and per partes in definite integral.
6. Geometrical applications of definite integral - length of a curve, volume and surface of a rotating body.
7. Differential calculus of functions of two variables: its definition, graph, limits and continuity, partial derivatives of the first and higher order.
8. Equation of a tangential plane and normal to a surface. Local extrema of functions of two variables.
9. Constrained extrema of functions of two variables. Function given implicitly and its derivative.
10. Ordinary differential equations of first order: General, particular and singular solutions. Separable equations.
11. Homogeneous differential equations.
12. 1st order linear differential equation - method of variation of arbitrary constants
13. 2nd order linear differential equation with constant coefficients - method of undetermined coefficients.
14. Reserve
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.