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
Course slides (updated: 5/Mar/2021)
Exams
Practice midterm exam - Solutions (updated: 25/Jan/2021)
Practice final exam - Solutions (updated: 22/Feb/2021)
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.