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Various lecture notes in Adobe .pdf format.

Caveat Lector!

### Some lectures on topics connected to magnetic resonance imaging

The
material in the lectures is all copyrighted by Charles L. Epstein,
except as noted. Material copyrighted by other authors may only be used
for teaching a research purposes.- A lecture presented at the 2008 ISMRM meeting on RF-pulse synthesis.
- A series if three lectures on MRI presented at the Workshop on Inverse Problems, MSRI, Berkeley, CA, August 2010.

- Lecture 1: Magnetic Resonance Imaging: Basic Concepts.
- Lecture 2: Fourier Transform, Imaging and Contrast.
- Lecture 3: Diffusion, and Susceptibility.

The second edition of "Introduction to The Mathematics of
Medical Imaging" is now available from SIAM

The webpage for Math 584, 2006.

Lecture Notes on indices, relative indices and Toeplitz
operators. Summer 1999
Indices and relative indices in CR
and
contact geometry

Notes on related topics

Several complex variables
Title page
Section 1
Section 2
Section 3

Pseudodifferential operators
- Basic analysis for students of
pseudodifferential
operators

- Elliptic boundary value problems for the
Laplace
operator
- Pseudodifferential Methods for Boundary
Value Problems. This corrects an error in the published version in
Fields Institute Communications, vol. 52.

Functions of a complex variable
One complex variable Courtesy of Jeff
Achter.

An elementary lecture on the design of selective RF-pulses in
Magnetic Resonance Imaging.
A Lecture on Selective RF-pulses in MRI
from BE581, Spring 2003.

If you have any comment or corrections please send them to me at cle@math.upenn.edu . Thanks
very much!