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 *[[attachment:Slides_AnalisisI_2021.pdf|Course slides]] (updated: 3/Mar/2021)  *[[attachment:Slides_AnalisisI_2021.pdf|Course slides]] (updated: 5/Mar/2021)

Analisis I - 2021

  • Professor: Leandro Gorno (<leandro.gorno AT fgv DOT br>)

  • Monitor: Gil Navarro (<gilnavarro05 AT gmail DOT com>)

  • Horários:
    • Aulas: Mondays, Wednesdays, and Fridays 11-13.

    • Monitorias: Thursdays 14-

News

  • Due to the ongoing COVID-19 pandemics, lectures will be delivered online through Zoom. I sent an email with access information on 9/JAN/2021. Alternatively, check E-class for the course Zoom links and password.

Materials

Exams

Class schedule (tentative)

  • 11/1. Introduction to the course. Sets and functions.
  • 13/1. Uncountable sets. The real numbers.
  • 15/1. More on the real numbers.
  • 18/1. More on cardinality. Intervals and the nested cell property. The Cantor set.
  • 22/1. Mathematical spaces.
  • 25/1. Topology on R^n.
  • 27/1. Neighborhoods, Nested cells.
  • 29/1. Bolzano-Weierstrass. Compactness and Heine-Borel.
  • 1/2. More on Heine-Borel and applications.
  • 3/2. Sequences. Limits. Monotone convergence.
  • 4/2. Midterm exam.
  • 5/2. Subsequences. Cauchy sequences. Cauchy criterion. Completeness. Sequential compactness.
  • 8/2. Limsup and liminf.
  • 10/2. Sequences of functions. Uniform convergence. Continuous functions. Local properties.
  • 12/2. Linear functions. Global characterization of continuity. Preservation of connectedness.
  • 22/2. Preservation of compactness. Weierstrass extreme value theorem. Uniform continuity. Weierstrass approximation theorem.
  • 24/2. Sequences of functions. Limits of functions. Arzela-Ascoli.
  • 26/2. Differentiable functions. Derivatives. Mean-value theorem.
  • 1/3. Taylor's theorem. Remainder.
  • 3/3. The Riemann-Stieltjes integral.
  • 5/3. More on the Riemann-Stieltjes integral.
  • 11/3. Final exam.

Problem Set

MD/AnalisisI/2021 (last edited 2021-03-05 11:04:16 by LeandroGorno)