Special functions independent study
Reading, assignments, and due dates for assignments are listed below.
Throughout, AW refers to Arfken and Weber, sixth edition.
Fri May 21
Fri May 28
Fri June 4
In class we showed that if f (z ) is a holomorphic function with simple isolated zeroes located
at a1 , a2 , , none of the ai zero, then f (z ) could be written in terms of f (0), f (0), and the
f (z ) = f (0) exp z
f (0) n
1. An example of convolution
Consider a function
f (x) = cos x + cos 3x
(exp(ix) + exp(ix) + (exp(3ix + exp(3ix)
Imagine passing this function through a low-pass lter, that multiplies the coecients of 1,
exp(ix) by 1, and multiplies all other Fo
(1 2xt + t2 )
for = 0.
The Gegenbauer polynomials Cn) (x) are also known as ultraspherical polynomials (see
Arfken-Weber end of section 12.1).
The Gegenbauer polynomials include
See [section 4.5] and  for more information.
An elliptic function is a single-valued doubly-periodic function of a single complex variable
which is analytic except at poles and whose only singularities in the nite plane
Asymptotic series play a crucial role in understanding quantum eld theory, as Feynman diagram
expansions are typically asymptotic series expansions. As I will occasionally refer to asymptotic
series, I have included in this ap
Given a real-valued function f (x) on the real line, dene the Fourier transform of f (x) to be
f (k) =
f (x) exp(ikx)dx
f (k) exp(ikx)
Then it can be shown that
f (x) =
known as the in
See Arfken & Weber section 6.7 (mapping) or [sections 106-108] for more information.
A Riemann surface is a generalization of the complex plane to a surface of more than one
sheet such that a multiple-valued function on the
See Arfken & Weber pp 432-434 (in section 6.5 on Laurent expansions) for some of the
material below. Our description here will closely follow .
The intersection of two domains (regions in the complex plane) D1 , D2 , de
Syllabus, Fall 2009
HISTORY OF ECONOMIC THOUGHT
W. A. Schaffer
MWF 2, IC 109
TEXTS: (1) Todd G. Buchholz, New Ideas from Dead Economists, Revised
Edition, New York: Plume (Penguin Putnam, Inc.), 1999. (2) Robert L.
Heilbroner, The Wor
From Russian Site:
1. R. Ekelund, R.Herbert A History of Economic Theory and Method. McGraw Hill Publ. Co. 1990.
2. M. Blaug Economic Theory in Retrospect Cambridge University Press 1991
3. T. Negishi History of Economic Theory North-Holland 1989
ECONOMICS 4177: HISTORY OF ECONOMIC THOUGHT
History of Economic Thought
COURSE DESCTIPTION: ECON 4177. History of Economic Thought. (W) (3) (3G)
Prerequisites: ECON 1201 and 1202. History of economics as a science and