Introduction to Mathematical Analysis — MAN

  • Instructor:
    Zoltan Vidnyanszky
    Contact: zoltan dot vidnyanszky at
  • Prerequisites: Calculus
  • Text: class notes

Course description: The most important concepts, methods and applications of real analysis and the theory of metric spaces are covered, with an emphasis on examples and problem solving. The course is self-contained, the only prerequisite is calculus. We do not follow closely a single textbook, but for those who wish to consult, the relevant chapter numbers of the reference books will be given.


  • Review: Real numbers, numerical sequences.
  • Differentiation I.: Limit, continuity and differentiation of single variable, real functions. Mean value theorems. Applications.
  • Integration: Indefinite and Riemann integrals, inequalities, estimating sums with integrals.
  • Metric spaces: Euclidean spaces. Topology, convergence, continuity, compactness, connectedness, completeness, separability. The metric space C([a,b]).
  • Differentiation II.: Derivation of functions of several variables.
  • Infinite series: Numerical series, sequences and series of functions, power series and analytic functions.