310-2112/01 – Mathematics II (MII)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 5 |
| Subject guarantor | Ing. Petra Schreiberová, Ph.D. | Subject version guarantor | Ing. Petra Schreiberová, Ph.D. |
| Study level | undergraduate or graduate | | |
| | Study language | Czech |
| Year of introduction | 2019/2020 | Year of cancellation | 2022/2023 |
| 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.
Teaching methods
Lectures
Individual consultations
Tutorials
Other activities
Summary
Integral calculus of function of one real variable: the indefinite and definite
integrals, properties of the indefinite and definite integrals, application in
the geometry and physics. Differential calculus of functions of several
independent variables. Ordinary differential equations of the first and the
second order.
Compulsory literature:
Recommended literature:
James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456
Additional study materials
Way of continuous check of knowledge in the course of semester
zápočet
za zpracování zadaného programu může student získat až 20 bodů
zkouška
Kombinovanou zkoušku tvoří praktická část (60 minut, příklady) a teoretická část (20 minut, teoretické otázky).
E-learning
http://mdg.vsb.cz/portal/m2/index.php
Other requirements
There are no further requirements put on the student.
Prerequisities
Co-requisities
Subject has no co-requisities.
Subject syllabus:
I Integral calculus of functions of one variable
Antiderivatives and indefinite integral. Integration of elementary functions, integration by substitutions, integration by parts, integration of rational functions, definite integral and methods of integration, Geometric application of definite integrals.
II Differential calculus of functions of two or more real variables
Functions of two or more variables, graph, partial derivatives of the 1-st and higher order, total differential of functions of two variables, tangent plane and normal to a surface, extrema of functions.
III Ordinary differential equations
General, particular and singular solutions, separable homogeneous equations, homogeneous equations, linear differential equations of the first order, method of variation of arbitrary constant, 2nd order linear differential equations with constant coefficients, linearly independent solutions, Wronskian, fundamental system of solutions,
2nd order LDE with constant coefficients - method of variation of arbitrary constants, method of undetermined coefficients, application of differential equations.
Conditions for subject completion
Conditions for completion are defined only for particular subject version and form of study
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction