Schwarz-Christoel transformations
It is helpful to have available systematic ways to nd a variety useful conformal mappings. Our text treats one such method: bilinear transformations. Here we study a second:
Schwarz-Christoel transformations. These are di

642:528
ASSIGNMENT 10
SPRING 2012
This is a long assignment which deserves a little more time: Turn in starred problems
Thursday 04/05/2012.
Section 24.4: 3 (b), (c), (k); 5 (a), (b), (e)*.
Section 24.5: 1. (a); 2 (b), (d), (e)* (h), (i)*; 3 (f), (j), (k)

642:528
ASSIGNMENT 11
SPRING 2012
Turn in starred problems Thursday 04/19/2012.
1
(1 + y (x)2 ) dx, subject to the
1 . Consider the problem of nding extrema of I (y ) =
0
conditions y (0) = y1 , y (1) = y2 .
(a) Determine the Euler-Lagrange equation for t

642:528
ASSIGNMENT 12
SPRING 2012
This assignment will not be collected.
Posted with this assignment is a scan of a page from Methods of Applied Mathematics, by
Francis Hildebrand (Dover Publications, New York, 1992). Some of the listed problems
are from

642:528
ASSIGNMENT 8
SPRING 2013
Turn in starred problems Tuesday 3/26/2013.
Section 23.4: 3. (c)*, (d), 4* (see below; you are asked to do a little more)
Section 23.5: 1. (a), (d), (e), (k)*, 2, 3 (a)*, (b)*, (c), (d), 4 (a)*, (b)
Hints and instructions:

642:528
ASSIGNMENT 6
SPRING 2013
Recall that Exam 1 is scheduled for Tursday, February 28. It will cover our work
through February 22, that is, through Chapter 22, omitting Section 22.5. More information
is posted on the web page.
Turn in starred problem

642:528
ASSIGNMENT 5
SPRING 2013
Recall that Exam 1 is scheduled for Tursday, February 28. It will cover our work
through February 21, that is, through Chapter 22, omitting Section 22.5.
Turn in starred problems Tuesday 2/26/2013.
Section 22.4: 4 (e)*, (g

642:528
ASSIGNMENT 3
SPRING 2013
Turn in starred problems Tuesday 2/12/2013.
Greenberg, Section 21.5: 5 (a), (b)*, 7, 9 (extra credit)*, 10 (a), (e)*, 12 (b)*,
14 (a), 15 (b)*, (c), (d)*. See instruction 1 below for 5(b) and 10(e).
If you do the extra cre

642:528
ASSIGNMENT 2
SPRING 2013
Turn in starred problems Tuesday 01/05/2013. Note that the three extra problems
2.A2.C are to be turned in. Homework must be stapled.
Greenberg, Section 21.3: 2 (b), (f)*, 9 (e), 12, 13*
Section 21.4: 11 (c), (e)*, (f), 13

Appendix: More on Schwarz-Christoel transformations
In this appendix we want to ll in several gaps in our discussion of the SchwarzChristoel transformation.
Recall that we argued that if we want to send the n (nite) points z1 , . . . , zn on the
real axis