230-0202 – Mathematics II (BcM II)

Mathematics is essential part of education on technical universities. It should be considered rather the method in the study of technical subjects than a goal. The aim of the subject is therefore to teach students not only basic mathematical knowledge, procedures and methods, but also to deepen their logical thinking. Students should learn to analyze a problem, distinguish the essential from the unessential, propose a solution procedure, check individual steps of the solution, generalize the conclusions, evaluate the correctness of the results with respect to the given conditions, apply tasks to solving technical problems, and understand that mathematical methods and thought processes are applicable in areas other than mathematics.

The course includes three chapters – integral calculus of functions of one real variable, introduction to differential calculus of functions of two real variables and ordinary differential equations. The aim of the first chapter is to master the basic techniques of integration and, above all, to become familiar with the geometric and physical applications of the definite integral. The second chapter deals with the basics of differential calculus of functions of two variables, creating a geometric idea of ​​a graph, determining local extrema and the tangent plane to a surface. The third chapter introduces the basic types of ordinary differential equations and their solutions.

Hass, J.R.; Heil, C.E.; Bogacki, P.; Weir, M.D.: Thomas' Calculus, 15th Ed., Pearson, 2023. Kreml, Pavel: Mathematics II, VŠB – TUO, Ostrava 2005, http://mdg.vsb.cz/portal/en/Mathematics2.pdf Volná, J.; Volný, P.: Worksheets for Mathematics II, VŠB-TUO, 2021; http://mdg.vsb.cz/portal/en/Mathematics2_worksheets.pdf

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.