3104
Comment:

← Revision 51 as of 20210305 11:04:16 ⇥
3104

Deletions are marked like this.  Additions are marked like this. 
Line 14:  Line 14: 
*[[attachment:Slides_AnalisisI_2021.pdfCourse slides]] (updated: 3/Mar/2021)  *[[attachment:Slides_AnalisisI_2021.pdfCourse 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 1113.
Monitorias: Thursdays 14
News
 Due to the ongoing COVID19 pandemics, lectures will be delivered online through Zoom. I sent an email with access information on 9/JAN/2021. Alternatively, check Eclass 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. BolzanoWeierstrass. Compactness and HeineBorel.
 1/2. More on HeineBorel 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. ArzelaAscoli.
 26/2. Differentiable functions. Derivatives. Meanvalue theorem.
 1/3. Taylor's theorem. Remainder.
 3/3. The RiemannStieltjes integral.
 5/3. More on the RiemannStieltjes integral.
 11/3. Final exam.