Math 254N
Assignment 17, Winter 2014
Due at 3:00 PM Wednesday, March 12th
1. For the following exercises, assume the following situation: The position of an ant crawling along a metal plate is
given by r(t) = t2 , 2t , where t is in minutes and the compon
Math 254N
Assignment 16, Winter 2014
2
1. Show that u(x, t) = sin(nx)en
t
Due at 3:00 Monday, March 10th
satises the one-dimensional heat equation
2u
u
.
=
t
x2
2. In this exercise you will be considering a region in three dimensional space. Assume the di
Math 254N
Assignment 13, Winter 2014
Due at 3:00 Wednesday, February 26th
1. For this exercise let T (x, y, z ) = x2 y + yz , where x, y and z are in feet and T is temperature in degrees
Celsius.
(a) Find the rate of change of T at (1, 3, 2), in the direc
Math 254N
Assignment 14, Winter 2014
Due at 3:00 PM Friday, February 28th
Show work for everything!
1. In this exercise you will nd the absolute minimum and maximum values of f (x, y ) = 2x2 xy +y 2 7y on
the rectangle bounded by 0 x 3, 0 y 5.
(a) Sketch
Math 254N
Assignment 18, Winter 2014
Due at 3:00 PM Thursday, March 12th
1. For the following exercises, assume the following situation: The position of a y buzzing around
in three-space is given by r(t) = t2 , 2t, t3 + 5t , where t is in seconds and the