subject	Analysis
lecturers	Dr. Faragó István, professor
credits	2+1=4
period	1
curriculum	Sets, relations, functions. Real numbers. Number sequences (convergence, operations with convergent sequences, Cauchy sequences, partial limit, Cantor theorem. Continuity and limit of functions. Continuous functions on an interval, Bolzano’s theorem, Weierstrass’ theorem, the continuity of the inverse function. Differentiable functions. Mean value theorem. Local extreme values, monotonicity, convexity. Riemann integral. Integrable functions, mean value theorem. Primitive functions, Newton-Leibniz theorem. Jordan measure, Cantor set, null sets under Lebesque measure, the necessary and sufficient condition of Riemann integrability. Lebesgue integral.
literature	I. Mezei, I Faragó, P. Simon, Á. Havasi: Introductory Course in Analysis, 2013.
form of tuition	lectures, practical exercises
mode of assessment	Written exam, reporting