## Repetition of Mathematics 2

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Course Unit Code Number of ECTS Credits Allocated Type of Course Unit * 230-0222/01 1 ECTS credits Optional First Cycle Second Year Winter Semester Face-to-face Czech Course succeeds to compulsory courses of previous semester KRE40 doc. RNDr. Pavel Kreml, CSc. Repetition of Mathematics 2 is intended for students who, for whatever reasons, fail the exam of Mathematics II and are interested in passing this exam. Its content essentially coincides with the content of the course Mathematics I. The aim is to enable better understanding of mathematics by the solving of concrete examples and problems. Repetition will focus on the practical part of the exam and they will be solved examples matching the written part of the exam. Mathematics is an 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 analyse problems, distinguish between important and unimportant, suggest a method of solution, verify each step of a method, generalize achieved results, analyse 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. 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. Kreml, Pavel: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X 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/M/ www.studopory.vsb.cz/ 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 mdg.vsb.cz/M/ www.studopory.vsb.cz/ Individual consultations, Tutorials Credit Credit