Math 402 – Modern Analysis, Winter 2017


Instructor: Anatolii Grinshpan
Office hours:  Tu 12-1 and Th 12-2, Learning Terrace.

Course information    Academic calendar    Tutoring center  

Jan   9.  The intermediate value theorem and Darboux’s theorem.

Jan 11.  Blancmange function: construction.

Jan 13.  Blancmange function: properties.

Reading: 5.2, 5.4. Problems.

 

Jan 16.  MLK day.

Jan 18.  Survival of surnames.

Jan 20.  Quiz 1 (5.2, 5.4).

Reading: 6.1, 6.2. Problems.

 

Jan 23.  Survival of surnames. Functional sequences.

Jan 25.  Pointwise convergence vs uniform convergence.

Jan 27.  Quiz 2 (6.1, 6.2). Problems.

 

Jan 30.  Uniform convergence and differentiation. Notes.

Feb  1.   Series of functions. Reading: 6.3, 6.4.

Feb  3.   Midterm 1: 5.4, 6.1-6.4.

 

Feb  6.  Uniform convergence and integration. Notes.

Feb  8.  Power series. Abel’s theorem. Notes.

Feb 10. Taylor polynomials. Lagrange’s remainder term. Notes.

Reading: 6.5, 6.6. Problems.

 

Feb 13. Quiz 3 (6.5, 6.6). Lagrange’s remainder term.

Feb 15. Convergence of Taylor series.

Feb 17. Weierstrass’ approximation theorem. Notes.

Reading: 6.6, 6.7. Problems.

 

Feb 20. The Riemann integral.

Feb 22. Properties of integrable functions.

Feb 24. Quiz 4 (7.1-7.3).

Reading: 7.1-7.3. Problems.

 

Feb 27. Properties of integrable functions. Notes.

Mar  1. The Fundamental Theorem of Calculus. Example. Reading: 7.4, 7.5.

Mar  3. Midterm 2: 6.5-6.7, 7.1-7.5.

 

Mar  6.  Outer content. Notes. Cantor sets.

Mar  8.  Lebesgue null sets. Set of discontinuities. Worksheet.

Mar 10. Lebesgue’s criterion for Riemann integrability. Notes.

Reading: 7.6, 7.7. Problems.

 

Mar 13. Lebesgue’s criterion. Fσ and Gδ sets. Example.

Mar 15. Quiz 5 (7.6). Metric spaces.

Mar 17. Baire Category Theorem. Meager sets. Notes. Example.

Reading: 3.5, 8.2.

 

Mar 20. Questions session.

Mar 21. Office hours: 1-2PM, Korman 228.

Mar 23. Final exam (all lectures): 8-10AM, Curtis 456.