MATH 3220
SECOND HOMEWORK ASSIGNMENT
Sept. 5, 2000
A. Treibergs
Due Sept. 12, 2000
Please write up the following exercises from the text "Introduction to Analysis, Second Edition" by William Wade, Prentice Hall 1999.
244[1c,2b,6], 251[2,8].
Here are the equivalent exercises for those using the First Edition:
251[2c,1d,4],
Let f(x,y)=(xy, x+y,x
^{2}
-y
^{2}
). Using Definition 6.4 prove that f is differentiable on
R
^{2}
and its total derivative is given by
Df(x,y) =
[
y
x
1
1
2x
-2y
]
Let X and Y be Euclidean Spaces. Show that if T ∈ £(X,Y) is linear then T is differentiable everywhere on X with
DT(a) = T for all a ∈ X.