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Mathematics II

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code230-0306/01
Number of ECTS Credits Allocated4 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
STR78Mgr. Jakub Stryja, Ph.D.
CER365doc. Ing. Martin Čermák, Ph.D.
VOL18RNDr. Jana Volná, Ph.D.
VIT0060Mgr. Aleš Vítek, Ph.D.
Summary
Mathematics II is divided in three parts:
1. Integral calculus of functions of one real variable - indefinite integral, some properties, elementary methods of integration.
2. Differential calculus of functions of two real variables - the partial derivations, extremes of functions of two variables.,
3. Ordinary differential equations - ordinary differential equation of the 1st and 2nd order.

Learning Outcomes of the Course Unit
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.
Course Contents
1. Integral calculus: antiderivative and indefinite integral for functions of one variable.
2. Integration methods - substitution, integration by parts.
3. Integration of rational functions, irrational functions, trigonometric functions.
4. Definite integrals: basic concepts, properties, Newton-Leibniz rule.
5. Substitution method and integration by parts for the definite integral.
6. Geometric and physical application of definite integrals.
7. Differential calculus for functions of two variables: definition, domain, limits and continuity.
8. Partial derivatives of first order and higher orders. Total differential.
9. The equation of the tangent plane and of the normal.
10. Extrema of functions of two variables.
11. Implicit function and its derivatives.
12. Ordinary differential equation of the 1st order: types of solutions, separable, homogeneous and linear.
13. Linear differential equations of the 2nd order with constant coefficients: variation of constants, determination of coefficients.
14. Linear differential equations of higher orders.
Recommended or Required Reading
Required Reading:
[1] Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications. D.C.Heath
and Company, Lexington1990. ISBN 0-669-21145-1
[2] James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-
201-1805456
[3] http://mdg.vsb.cz/portal/en/Mathematics2.pdf
[1] Vrbenská, H., Bělohlávková, J.: Základy matematiky pro bakaláře II.
Skriptum VŠB-TUO, Ostrava 1998. ISBN 80-7078-545-4
[2] Vlček, J., Vrbický, J.: Diferenciální rovnice (Matematika IV). VŠB-TU, 1998
[3] http://www.studopory.vsb.cz/studijnimaterialy/MatematikaII/m2.pdf
[4] http://mdg.vsb.cz/portal/
[5] Kreml, Pavel: Mathematics II, Ostrava 2005, 80-248-0798-X.
[6] http://mdg.vsb.cz/portal/en/Mathematics2.pdf
Recommended Reading:
[1] Buchanan, James., L.,Turner, Peter., R.: Numerical Methods and Analysis.
McGraw-Hill, Inc. New York 1992. ISBN 0-07-008717-2
[1] Škrášek, J., Tichý, Z.: Základy aplikované matematiky I,II. SNTL,Praha 1990.
[2] Rektorys, K.: Co je a k čemu je vyšší matematika. ACADEMIA, Praha 2001.
ISBN 80-200-0883-7
[3] Píšová, D. a kol.: Diferenciální počet funkcí více proměnných. Skripta VŠB,
Ostrava 1989.
Planned learning activities and teaching methods
Lectures, Individual consultations, Tutorials
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit20 10
        ExaminationExamination80 (80)30
                Písemná zkouškaWritten examination60 25
                Ústní zkouškaOral examination20 5