The aftermath of Bell's tablet PC lectures
These are the lecture notes and videos of Bell's
tablet PC lectures.
Lecture 1
on 08-25 and the
video
Introduction, new ways to think about complex analysis
Lecture 2
on 08-27 and the
video
Poisson and Dirichlet
Lecture 3
on 08-29 and the
video
Harmonic functions
Lecture 4
on 09-03 and the
video
The averaging property
Lecture 5
on 09-05 and the
video
The "dee bar" operator
Lecture 6
on 09-08 and the
video
Using the "dee" and "dee bar" operators
Lecture 7
on 09-10 and the
video
A dee-bar proof of the Mittag-Leffler theorem
Lecture 8
on 09-12 and the
video
Solving the inhomogeneous Cauchy-Riemann equations on the complex plane
Lecture 9
on 09-15 and the
video
Runge's theorem and solving the d-bar problem
Lecture 10
on 09-17 and the
video
The Cauchy-Kovalevskaya theorem
Lecture 11
on 09-19 and the
video
More on the Cauchy-Kovalevskaya theorem
Lecture 12
on 09-22 and the
video
The Cauchy transform
Lecture 13
on 09-24 and the
video
Boundary behavior of the Cauchy transform
Lecture 14
on 09-26 and the
video
Applications of the improved Cauchy Integral Formula
Lecture 15
on 09-29 and the
video
Free theorems from the u=h+H result
Lecture 16
on 10-01 and the
video
The Plemelj formula
Lecture 17
on 10-03 and the
video
The adjoint of the Cauchy transform
Lecture 18
on 10-06 and the
video
The adjoint of the Cauchy transform, part 2
Proof of Weyl's lemma (see page 75 of the book) on 10-08
Lecture 19
on 10-10 and the
video
The Kerzman-Stein kernel
Lecture 20
on 10-15 and the
video
Consequences of Kerzman-Stein
Lecture 21
on 10-17 and the
video
The Szegö kernel
Lecture 22
on 10-20 and the
video
The Riemann map and the Szegö kernel
Lecture 23
on 10-22 and the
video
Solving the Dirichlet problem using the Szegö projection
Lecture 24
on 10-24 and the
video
Hardy space history
Lecture 25
on 10-27 and the
video
Miscellaneous things
Lecture 26
on 10-29 and the
video
The Bergman space
Lecture 27
on 10-31 and the
video
The Bergman kernel
Lecture 28
on 11-03 and the
video
The Bergman projection
Lecture 29
on 11-05 and the
video
The Bergman projection and the Green's operator
Lecture 30
on 11-07 and the
video
More properties of the kernel functions
Lecture 31
on 11-10 and the
video
Not so good proofs versus better proofs
Lecture 32
on 11-12 and the
video
Domains with holes versus no holes
Lecture 33
on 11-14 and the
video
The Hopf lemma and consequences
Lecture 34
on 11-17 and the
video
The normal derivative of a harmonic function
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