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

Course Unit Code | 230-0202/01 | |||||
---|---|---|---|---|---|---|

Number of ECTS Credits Allocated | 5 ECTS credits | |||||

Type of Course Unit * | Compulsory | |||||

Level of Course Unit * | First Cycle | |||||

Year of Study * | First Year | |||||

Semester when the Course Unit is delivered | Summer Semester | |||||

Mode of Delivery | Face-to-face | |||||

Language of Instruction | Czech, English | |||||

Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester | |||||

Name of Lecturer(s) | Personal ID | Name | ||||

KRE40 | doc. RNDr. Pavel Kreml, CSc. | |||||

VOL06 | RNDr. Petr Volný, Ph.D. | |||||

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. | ||||||

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 | ||||||

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 and physical application of definite integrals. 6. 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. 7. Total differential of functions of two variables, tangent plane and normal to a surface, derivation of implicit functions. 8. Extrema of functions. 9. Ordinary differential equations. General, particular and singular solutions. Separable and homogeneous equations. 10. Linear differential equations of the first order, method of variation of arbitrary constant. Exact differential equations. 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. Reserve. 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. 13. Method of undetermined coefficients. 3rd test (differential equations). 14. Reserve. | ||||||

Recommended or Required Reading | ||||||

Required Reading: | ||||||

Kreml, Pavel: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X
http://mdg.vsb.cz/portal/en/Mathematics2.pdf | ||||||

Vrbenská, H.: Základy matematiky pro bakaláře II. Skripta VŠB - TU, Ostrava
1998. Pavelka, L. – Pinka, P.: Integrální počet funkce jedné proměnné. Skripta VŠB- TU, Ostrava 1999. Vlček, J. – Vrbický, J.: Diferenciální rovnice. Skripta VŠB-TU, Ostrava 1997. Píšová, D. a kol.: Diferenciální počet funkcí více proměnných. Skripta VŠB, Ostrava 1989. Škrášek, J. a kol.: Základy aplikované matematiky I. a II. SNTL, Praha 1986. mdg.vsb.cz/portal/ www.studopory.vsb.cz/ | ||||||

Recommended Reading: | ||||||

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 | ||||||

http://mdg.vsb.cz/portal/
http://www.studopory.vsb.cz/studijnimaterialy/MatematikaII/m2.pdf http://mdg.vsb.cz/portal/m2/PV_PracovniListyM2.pdf http://www.studopory.vsb.cz/studijnimaterialy/Sbirka_uloh/pdf/suzm.pdf | ||||||

Planned learning activities and teaching methods | ||||||

Lectures, Individual consultations, Tutorials, Other activities | ||||||

Assesment methods and criteria | ||||||

Task Title | Task Type | Maximum Number of Points (Act. for Subtasks) | Minimum Number of Points for Task Passing | |||

Credit and Examination | Credit and Examination | 100 (100) | 51 | |||

Credit | Credit | 20 | 5 | |||

Examination | Examination | 80 (80) | 30 | |||

Písemná zkouška | Written examination | 60 | 25 | |||

Ústní zkouška | Oral examination | 20 | 5 |