MATH 423:01 FALL 2001 -- PROBLEM SHEET 4

For The Rules, see problem sheet 1. Your solutions for the problems on this sheet are due in class on the last day that the class meets, or delivered to the Mathematics Undergraduate Office, Hill Center 303 (Busch), no later than 4PM on the last day of classes. Do NOT slide them under the instructor's office door; hand them to a human or presume them lost.

Since no solutions for problems in Strauss's Ch. 7 have yet been posted, we can use some of those problems for this problem sheet. Namely:

Assigned Problems from Strauss's Ch. 7
Section Number Remarks
§7.1 #2 p. 174.  You may do the 2-dimensional version of this if you wish.
§7.1 #3 p. 175.
§7.2 #2 p. 178.  You may do the 2-dimensional version of this if you wish.  Hints: look at the reasoning linking formulas (15.01) through (15.04) in the cvlap2 notes (dim = 2) or the representation formula of Strauss's pp. 176-178 (dim = 3), and modify the reasoning to cover the case in which u(.) is not harmonic. 
§7.4 #1 p. 186.
§7.4 #12 p. 187.
§7.4 #19 p. 188. The solution given here is wrong in my copy of the text (it's just an oversight).  Give a correct solution. For the form of the Laplace operator in n-dimensional space acting on a function of r (= radial distance to the origin) only, see the posted solution for problem #6 in §2.2.