subject	Mathematics 3
lecturers	Dr. Faragó István, professor
credits	2+2=4
period	3
curriculum	Metric spaces. Topological notions and convergence in metric spaces, complete metric spaces. Continuous mappings in metric spaces, fixpoint theorem. Vector spaces, linear independence, basis. Linear operators in vector spaces. Normed spaces. Topological notions in normed spaces. The C[a,b] space. Continuous and linear mappings in normed spaces. Banach spaces. Operator norms in normed spaces (supremum norm and its properties). Matrices, linear operators in finite dimensional spaces. Differentiation in normed spaces, operations. Directional derivative. Partial derivatives. Higher-order derivatives. Taylor formula. Extreme values of multi-variable functions. Jordan curves. Connected domains, convexity. Arc length, rectifiable curves. Line integral and its properties. Newton-Leibniz theorem.
literature	I.Mezei, I Faragó, P. Simon, Á. Havasi: Introductory Course in Analysis, 2013. M. Mincsovics, Á. Havasi, T. Haszpra: Matematikai példatár földtudományi szakosoknak, 2013.
form of tuition	lectures, practical exercises
mode of assessment	Written exam, reporting