Courses

Taylor-Maclaurin theorem. Taylor polynomial of n-order, Taylor formula with Lagrange remainder, applications of Taylor polynomial to approximation problems. Derivative and indefinite integral. Definition of the indefinite integral, basic properties, integration with change of variable, integration by factors, integration of rational functions, integration of basic types of functions. Definite integral (Riemann integral). Definition, properties, integrability criteria, mean value theorem for definite integrals, inequalities between definite integrals, Fundamental Theorem of Infinitesimal Calculus for the calculation of the definite integral, change of variable in the definite integral. Applications of definite integrals. Calculation of area of ​​a region, volume of a solid of revolution and arc length. Epicyclic integrals. Vector functions, parametric representation of curves, integrals over curves. Generalized integrals. Types of generalized integrals and their calculation, basic properties, convergence criteria for generalized integrals of non-negative functions (comparison criterion, limit criterion, etc.), absolute convergence of generalized integrals, change of variable in the generalized integral. In order to highlight the special elements of pedagogical and teaching competence contained in the course, emphasis is placed on its historical development, the development of its cognitive subject, but also on its applications in technology and/or other sciences. Information: Renaming of the Course "Real Analysis II" in the Academic Year 2019-20.