310-2212/03 – Mathematics II (M II)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 6 |
| Subject guarantor | Mgr. Petr Otipka, Ph.D. | Subject version guarantor | RNDr. Jan Kotůlek, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | summer |
| | Study language | English |
| Year of introduction | 2023/2024 | Year of cancellation | |
| Intended for the faculties | FMT | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
The goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods.
Students should learn how to: analyze problems, suggest a method of solution, analyze correctness of achieved results with respect to given conditions,
aply these methods while solving technical problems.
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:
[1] KREML, P: Mathematics II, Ostrava 2005, 80-248-0798-X. http://mdg.vsb.cz/portal/en/Mathematics2.pdf
[2] JAMES, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456.
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
Course-credit
-participation on tutorials is obligatory, 20% of absence can be apologized,
-pass the written three tests
Point classification: 15-35 points.
Exam
Practical part of an exam is classified by 0 - 55 points. Practical part is successful if student obtains at least 20 points.
Theoretical part of the exam is classified by 0 - 10 points. Theoretical part is successful if student obtains at least 5 points.
Point quantification in the interval 100 - 91 90 - 81 80 - 71 70 - 61 60 - 51 50 - 0
ECTS grade A B C D E F
Point quantification in the interval 100 - 86 85 - 66 65 - 51 51 - 0
National grading scheme excellent very good satisfactory failed
E-learning
http://lms.vsb.cz
Other requirements
No special requirements.
Prerequisities
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1 Differential calculus of functions of two or more real variables. Functions of two or more variables, graph,
2 Partial derivatives of the 1-st and higher order.
3 Total differential of functions of two variables, tangent plane and normal to a surface, extrema of functions.
4 Integral calculus of functions of one variable. Antiderivatives and indefinite integral. Integration of elementary functions.
5 Integration by substitutions, integration by parts.
6 Integration of rational functions.
7 Definite integral and methods of integration.
8 Geometric and physical application of definite integrals.
9 Ordinary differential equations. General, particular and singular solutions. Separable equations.
10 Homogeneous equations. Exact equations. Linear differential equations of the first order, method of variation of arbitrary constant.
11 2nd order linear differential equations with constant coefficients, linearly independent solutions, Wronskian,fundamental
system of solutions.
12 2nd order LDE with constant coefficients - method of variation of arbitrary constants, method of undetermined coefficients.
13 Application of differential equations
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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