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Department of Physics

ΕΛΕ11

10ΕΛΕ11 Real Analysis

Course webpage:  https://eclass.uoa.gr/courses/MATH244

Course outline

Course content

  • Set theory, countability. Metric spaces. Topological notions. Equivalent metrics. Bounded sets.
  • Continuity of functions on metric spaces. Isometries. Lipschitz functions. Uniform continuity.
  • Completeness. Fixed point theorems and applications to differential equations. Cantor theorem, Baire theorem and applications.
  • Compactness. Separability. Cantor set.
  • Sequences and series of functions: Pointwise and uniform convergence, Weierstrass criterion, uniform convergence and continuity, integration and differentiation.
  • Continuous real functions in compact metric spaces: Weierstrass approximation theorem. The structure of the C(X) metric space.