Course Website

Math 6302: Analysis II

Lecture: MATH 6302-100
Room: Morton Hall 322
Time: MWF 9:40am -- 10:35am
Instructor: Marcel Bischoff
Office: Morton Hall 521
Office Phone: (740-59)3-1261
Office Hours: Mon & Wed: 10:45am-11:45am, Fri: 8:05-9:00am

Schedule

1. Mon 01/14:
• Syllabus
• Metric Spaces, Complete Metric Spaces, Normed spaces, Banach spaces.
• Section 9.1, 9.2, 9.4
2. Wed 01/16:
• Young inequality, Hölder inequality, Minkowski, inequality, $L^p(E)$ is a normed space.
• Section 7.2
3. Fri 01/18:
• $C([0,1])$ is a Banach spaces, Rapidly Cauchy sequences.
• $L^p(E)$ is a complete thus a Banach space
• Section 9.4, 7.3
4. Wed 01/23:
• Finishing of proof of $L^p(E)$ is complete
• Pointwise almost everywhere vs $L^p$ convergence
• Section 7.3
5. Fri 01/25:
• Definition of dense subset in a topological space, metric space, ...
• Separability of Metric Spaces
• Separability of $L^p(E)$ for $1\leq p <\infty$
• $L^\infty([0,1])$ is not separable
• Section 9.6, 8.1
6. Mon 01/28:
• Bounded Operators between Banach spaces
• Bounded Linear Functionals
• Bounded Linear Functionals on $L^p(E)$ from $L^q(E)$
• Quiz 01
• Section 8.1
7. Wed 01/28:
• Classes cancelled due to weather
• Quiz 02
• Riesz-Fischer Theorem
• Section 8.1
8. Fri 02/01:
• Classes cancelled due to weather
• Riesz-Fischer Theorem
• Section 8.1
• Quiz 02
9. Mon 02/04:
• Comparison of topologies (weak vs strong)
• Weaker and Stronger Topologies
• Weak topology on Banach spaces
• Weak convergence on Banach spaces
• Weak convergence on $L^p(E)$
• Section 8.2
10. Wed 02/06:
• Weak convergence on $L^p(E)$
• Riemann-Lebesgue Lemma
• Section 8.2
11. Fri 02/08:
0. Fri 05/03: 1:00pm-3pm: Final Exam

Ressources

• Tao - Analysis I (free eBook access through Alden Library)
• Tao - Analysis II (free eBook access through Alden Library)

Last update: 2019-02-27 18:27:16.