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 books.google.com Michiel Hazewinkel  1994  Preview AMS 1980 Subject Classification: 65D32 CHRISTOFFELSCHWARZ FORMULA 
The formula , '0 * = constituting an integral representation for a function f(z)
which defines a conformal mapping of the upper halfplane Imz>0 onto the
interior ... 

 books.google.com However, if the given region is a polygon there is an explicit formula, obtained
independently by H. A. Schwarz (1866) and E. B. Christoffel (1867), supplying the
conformal mapping of the upper halfplane Im z > 0 onto the interior plus ... 

 books.google.com 1.2 History 5 Elwin Bruno Christoffel (18291900) was born in the German town
of Montjoie (now Monschau) and was ... It was in Zurich that he published the first
paper on the SchwarzChristoffel formula, with the Italian title, "Sul problema ... 

 books.google.com This representation is called the SchwarzChristoffel transformation formula. This
formula was originally derived by Christoffel to solve a problem of 2dimensional
distribution of stationary temperature. It then found extensive application to ... 

 books.google.com From the formula and the fact that ip(z) < 1 on one side of 7 in D, we see that
IvKz)! ... The. SchwarzChristoffel. Formula. Suppose that D is a polygonal
domain, bounded by a finite number of straight line segments, and w = g(z) is a
conformal ... 

 books.google.com Now let a be an interior point of D. According to Theorem 5.12e, any function g
mapping the unit disk £ onto D and satisfying g(0) = a is given by the Schwarz
Christoffel (SC) formula, I"" n / W [1 1  Jo *=o \ Wk dw, (16.101) where c is a ... 

 books.google.com 1.7 SchwarzChristoffel mappings By SchwarzChristoffel mappings we mean the
family of methods that are based on the use of the wellknown Schwarz
Christoffel formula, the underlying theory of which is treated extensively in the
complex ... 

 books.google.com 5.2. SchwarzChristoffel. Formula. In the previous section we have seen how the
Riemann mapping function of a proper simply connected region can be extended
analytically to certain parts of the boundary. However there is no way we can ... 

 books.google.com Use the prevertices x1 D ; x2 D 1;x3 D 1; and x4 D ; where > 1: You can find an
equation involving as a variable that, chosen ... A simplification to the Schwarz
Christoffel formula that is frequently employed is to set one of the prevertices to
be 1, ... 

 books.google.com (iii) If the polygonal region is bounded, only n 1 of the n interior angles should be
included in the Schwarz–Christoffel formula. As an illustration, the interior angles
a1, a2, a3, and a4 are sufficient to determine the Schwarz–Christoffel formula ... 

 