AMCS/MATH 608: Analysis
Instructor: Charles L. Epstein
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This year the Analysis I-II sequence is being
redesigned to cover Complex Analysis, Real Analysis (Measure Theory),
and Functional Analysis. The first semester
introduction, at the graduate level, to functions of one complex
variable and the first half of real analysis.
For the first ten weeks, we cover the basic Cauchy
theory, we will focus on more analytic features of the subject,
highlighting its connection to PDE and Fourier analysis. As references
for complex analysis we use E. Stein and R.
Lars Ahlfors, Complex
Zeev Nehari, Conformal
Mapping. More advanced material on the d-bar equation can
be found in T. Napier and M. Ramachandran, An Introduction to Riemann
weeks 11-14 we begin our discussion of Real Analysis, which will be
followed by 4 more weeks in the second semester. In the first
semester we will cover Measure Theory and Lebesgue Integration in
Euclidean space. References for Real Analysis are Real Analysis by E.
Stein and R. Shakarchi, Real
Analysis by Gerald Folland, and Real Analysis by H.
A problem set
assigned every week on Tuesday, due the following week on Tuesday. I
very much prefer that students do the
alone. We may
have midterm and final exams.
- The class meets on TuTh from 1:30 to 3:00 in room 4C8 of
- Tentatively my office hour will be Mondays 3:30-5:00PM.
Contact me by e-mail for an
appointment if you can not come during this time.
- My office in the Math Department is 4E7 DRL, tel. 8-8476.
- email: email@example.com.
Send e-mail if you have a question or need to contact me.
TA is Soum Nayak. His office is 3N2B in DRL, and e-mail is nsoum [@]
math [.] upenn [.] edu. His office hours are on Wednesdays from 2:00 to
- A quick review of analysis in Rn
- Complex analysis
- Analytic functions and Cauchy's theorems
- The residue theorem and the argument principle
- The Cauchy Riemann equations and harmonic functions
- The maximum principle and the three circle theorem
- The d-bar equation
- The Fourier transform, the Hilbert transform
- Conformal mapping and incompressible steady flow
- The Dirichlet and Neumann problems for harmonic functions
- Real Analysis
- Measurable sets
- Measurable functions
- The Lebesgue integral
- Fubini's theorem
- Problem set 0,
These problems in advanced
caclulus do not have to be handed in, but should be done this week, so
you are ready for our discussion of contour integration.
- Problem set 1, due
September 16, 2014.
- Problem set 2, due
September 23, 2014.
- Problem set 3, due
September 30, 2014.
- Problem set 4, due
October 7, 2014.
- Problem set 5, due October 21, 2014.
- Problem set 6, due October 28, 2014.
- Problem set 7, due November 11, 2014.
- Problem set 8, due November 18, 2014.
- Problem set 9, due November 25, 2014.
- Problem set 10, due December 9, 2014.
- Problem set 11, due December 16, 2014.
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