Department of Physics

10ΥΚΟ11 Analysis I and Applications

Course webpage:  https://eclass.uoa.gr/courses/PHYS234

Course outline

Course content

• Numbers (natural, rational, irrational). Mathematical induction. Basic inequalities. Bound of a set. Supremum and infimum of of a set.
• The field of real numbers. Bounded sets of numbers. Upper and lower bound. Completeness.
• Sequences. Series. Radius of convergence of power series.
• Continuous functions and their properties.
• Differentiation. The mean value theorem. Extrema of functions and Taylor theorem. Fundamental functions.
• Riemann integral (upper and lower bound of an integral). Integration techniques. Approximation of definite integrals.