714-0367/05 – Mathematics II (MII)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits4
Subject guarantorIng. Petra Schreiberová, Ph.D.Subject version guarantorRNDr. Petr Volný, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageEnglish
Year of introduction2016/2017Year of cancellation2019/2020
Intended for the facultiesFSIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
VOL18 RNDr. Jana Volná, Ph.D.
VOL06 RNDr. Petr Volný, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 12+4

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 mathematics.

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:

Kreml, P.: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X

Recommended literature:

Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications. D.C.Heath and Company, Lexington1990, ISBN 0-669-21145-1 James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456

Way of continuous check of knowledge in the course of semester

Course-credit -participation on tutorials is obligatory, 20% of absence can be apologized, -elaborate programs, -pass the written tests, Point classification: 5-20 points. Exam Practical part of an exam is classified by 0 - 60 points. Practical part is successful if student obtains at least 25 points. Theoretical part of the exam is classified by 0 - 20 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://www.studopory.vsb.cz http://www.vsb.cz/714 http://mdg.vsb.cz/wiki/index.php/MatematikaII

Další požadavky na studenta

more requierements are not

Prerequisities

Subject codeAbbreviationTitleRequirement
714-0365 ZM Basics of Mathematics Compulsory
714-0366 MI Mathematics I Compulsory

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Syllabus of lecture 1 Integral calculus of functions of one variable. Antiderivatives and indefinite integral. Integration of elementary functions. 2 Integration by substitutions, integration by parts. 3 Integration of rational functions. 4 Definite integral and methods of integration. 5 Geometric application of definite integrals. 6 Differential calculus of functions of two or more real variables. Functions of two or more variables, graph, 7 Partial derivatives of the 1-st and higher order. 8 Total differential of functions of two variables, tangent plane and normal to a surface, extrema of functions. 9 Ordinary differential equations. General, particular and singular solutions. Separable homogeneous equations. 10 Homogeneous 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. 13 2nd order LDE with constant coefficients - method of undetermined coefficients. 14 Application of differential equations Syllabus of tutorial 1 Course of a function of one real variable. 2 Integration by a direct method. Integration by substitution. 3 Integration by substitution. Integration by parts. 4 Integration of rational functions. 5 1st test (basic methods of integration). Definite integrals. 6 Applications of definite integrals. 7 Functions of more variables, domain, partial derivatives. 8 Equation of a tangent plane and a normal to a graph of functions of two variables. Derivation of implicit functions. 9 Extrema of functions. 2nd test (functions of two variables). 10 Differential equations, separable and homogeneous differential equations. 11 Linear differential equations of 1st order. Exact differential equations. 12 2nd order linear differential equations with constant coefficients. 3rd test (differential equations). 13 Method of undetermined coefficients. 14 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

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2018/2019 (B2341) Engineering P English Ostrava 1 Compulsory study plan
2017/2018 (B2341) Engineering P English Ostrava 1 Compulsory study plan
2016/2017 (B2341) Engineering P English Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner