Homework 7
Mathematics H264
Dr. Edgar
page 428 #12. Length of the graph of f on [a, b] is the length of the path c(t) = (t, f (t),
t [a, b].
(a) Since f is piecewise continuously dierentiable, the pat
Homework 6
Mathematics H264
Dr. Edgar
page 375 #10. A is a 2 2 matrix, nonzero determinant. Dene T (x) = Ax. Then T
takes parallelograms onto parallelograms.
Consider the parallelogram G with vertex p
Homework 4
page 224 #36. Function u is C 2 on the unit disk D, and strictly subharmonic 2 u > 0.
Show u cannot have its maximum in the interior of D.
Suppose u has its maximum at an interior point (x,
Homework 2
Mathematics H264
Dr. Edgar
April 10, 2009
page 127 #26. Show that f : Rn Rm is continuous if and only if the inverse image of
every open set is open.
We use the denition of continuous on pa
Exam 2 Answers
Mathematics H264
1.
Use the Riemann sum denition to compute the integral
rectangle [0, 1] [1, 1] and f is dened by f (x, y ) = x + y .
D
f (x, y ) dA, where D is the
Fix n N. Write x =