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.