714-0666/02 – Mathematics II (M II)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits6
Subject guarantorMgr. Jiří Vrbický, Ph.D.Subject version guarantorMgr. Jiří Vrbický, Ph.D.
Study levelundergraduate or graduate
Study languageCzech
Year of introduction1999/2000Year of cancellation2009/2010
Intended for the facultiesFMTIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
GAR10 RNDr. Eliška Gardavská
HAM73 Mgr. Radka Hamříková, Ph.D.
JAR71 Mgr. Marcela Jarošová
NIK01 Ing. Marek Nikodým, Ph.D.
OND10 Mgr. Ivana Onderková, Ph.D.
VRB50 Mgr. Jiří Vrbický, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+3
Part-time Credit and Examination 20+0

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

Differential calculus of functions of several independent variables. 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. Ordinary differential equations of the first and the second order.

Compulsory literature:

James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456. James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6.

Recommended literature:

Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications. D.C.Heath and Company, Lexington1990, ISBN 0-669-21145-1.

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://mdg.vsb.cz

Other requirements

Prerequisities

Subject codeAbbreviationTitleRequirement
714-0665 M I Mathematics I Compulsory

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 homogeneous 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. 13 2nd order LDE with constant coefficients - 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

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Occurrence in special blocks

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