Homework, MATH 411, Spring 2013
Homework is from our text (Fitzpatrick) unless indicated.
Homework is due at the beginning of class on the day listed
in the schedule of work.
Homework #1
10.1: 1,5,6,7 (Hint: Cauchy-Schwarz Inequality),9
10.2: 3, 4 (you could use Theorem 10.9)
Homework #2
10.3: 1,2 (but in 1,2 you do not need to justify your answers);
10,11
11.1: 1,4,9
Problem A
on the page of
Extra homework problems.
12.2: 1,3,15
Homework #3
11.2: 1, 6, 10
11.3: 3, 4,6,8
11.4: 1,3, 5
Homework #4
13.1: 1, 3a, 3c, 9
13.2: 1a, 3, 5, 8a, 11
13.3: 1ab, 7,8,9ab,11
Homework #5
14.1:
2,3,4,15
14.2: 1,2,9,10
14.3: 1ab, 4, 5, 11d
(Before doing 14.3.11d: compute the
polynomial p of degree at most 2 which
best approximates f near the origin,
where f is the map defined by
f(x,y) = cos(x-y+xy) as in 11d.
To do this you could plug x-y-xy
into enough (not many!) terms of the power
series for cos.)
Homework #6
15.2: 1,3, 8
Problem B from the
Extra homework problems
15.3: 1, 9, 11
Problem C from the
Extra homework problems
Homework #7
16.1: 3,5,13,14
(You can "explain analytically"
by showing the derivative matrix is not invertible
at (x_0,y_0).)
16.2: 3,5, 8
16.3: 1,2,7,11
Homework #8
17.1: 1,2,3,4,7,12
(For 12, you can use 11 without
proving 11.)
17.2: 2,3,5,9
Homework #9
17.3: 1, 3a, 4 [in 4, look for the simplest
linear example]
17.4: 4,7,9,13, 14
Problem D on the page of
Extra homework problems.
Homework #10
18.1: 10,14
18.2: 4,8,9
18.3: 5,9,10
Homework #11
19.1: 2c, 3,5,6,9
[For 19.1: With every iterated integral you use:
draw a sketch of the domain of integration,
with a line segment indicating the interval of
the first (inner) integration, and coordinate
axis markings indicating the lower and upper
limits of the inner integration.]
Homework #12
Problem E from the
Extra homework problems
19.2: 2, 3,7,8
[Hint on 2: do a linear change of coordinates to
reduce to an integral on the unit sphere, and then
use spherical coordinates there.]
[Hint on 3: consider change of variables with
cylindrical coordinates,
which is given by the rule sending
(r,theta , z) to
(r cos (theta) , r sin (theta), z) .
Check an appropriate determinant is nonzero
to justify this.]
19.3: 5