The cylinder z=x+y^2 plotted
using MAPLE.
Monday April 3rd
Solve:
Sec. 19.1: 15, 25
Sec. 19.2: 1, 5, 8, 9, 10, 13, 18, 21 a, 23
Solve, write
up and turn in:
Sec.
19.1: 14
Sec. 19.2: 12, 14, 16, 22, 29 a,b, 30 a
Tuesday April 4
Solve, write
up and turn in:
Sec.
19.2: 31, 32 a,c
Wednesday April 5
Solve, write
up and turn in:
Sec.
19.3: 3, 8, 13 (use whatever method you want), 15, 16, 17
1. Find
the differential of the function f(x,y,z)=x y^2 z^3
at the point (1,2,3).
2. Give
an example of a function in 2 or more variables which is
not differentiable at some point.
Thursday April 6
Solve, write
up and turn in:
1. Consider
the surface z=f(x,y) and a point P on this surface.
Consider a curve on the surface, passing through P.
Show that the tangent line to this curve is contained in the
tangent plane to this surface at P.
2.
You
may want to use this important fact above when solving problem 16
assigned yesterday.
3. Give
an example of a function in two or more variables which is
continuous
at some point
but it is not differentiable at that point.
(If
you provided such an example in problem 2. yesterday, just repeat it
here.)
4. Find the rate of change of the
function F(x,y,z)=x^2-xy+xz
at the point (1,2,0) in the direction of the vector i+j+k.
(Caution: you do need a unit vector in the stated direction
before using the formula.)
Sec.
19.3: 18
(remember the cone and its tangent planes we saw in class?)
Sec. 19.5: 1b,c,
2b, 10
Sec. 19.6: 1, 2, 4
Friday April 7
Solve, write
up and turn in:
Sec. 19.5: 4,
5, 8
Sec. 19.6: 5,
6, 7, 9, 14, 15, 16
Solve
the wave equation
a^2
d^2w/dx^2 - d^2w/dt^2 = 0
as follows.
a) Substitute
u=x+at, v=x-at and show
that the equation becomes d^2w/(du dv) =0.
b) Solve this equation.