05_22

Tutoring for H263

Monday 3:30 – 4:30

Tuesday 11:30 – 3:30

Wednesday 11:30 – 12:30

Thursday 11:30 – 3:30

Final exam:

The write-ups are due Wednesday May 31.

Five problems will be graded (2 points each).

Find dA on a sphere radius a using a parametrization inspired by spherical coordinates

and using the formula dA= | Ru X Rv | du dv.

21.4: 15 (find the flux through direct calculation)

21.4: 1a,e 3, 5, 7, 9, 13

21.4: 6, 8, 15 (using Gauss's theorem)

Also: Calculate the surface integral

S

of the function f(x,y,z)=xyz where the surface S is the triangle

with vertices A=(1,0,0), B=(0,2,0), C=(0,0,3).

1. Consider the curve given parametrically by :x= cos(theta), y=sin(theta), z=theta, for 0<theta<4 Pi.

a. Show that the curve lies on the surface of the cylinder x^2+y^2=1.

b. Sketch the curve.

c. Calculate the flow of the field F=xi+yj+zk along the curve (i.e. the line integral of F. dR).

2. Find the flow of the vector field above along the segment beteen the points (1,2,3) and (0,6,0).

3. Consider a planar vector field F, which is continuously differentiable at all points in the plane.

Show that if curl F=0 (in which case we say that F is irrotational) then the integral of f along any

closed (simple, piecewise smooth) curve in the plane is zero.

21.5: 4, 5, 6, 7, 9

21.5: 1, 11

Review Chapter 21.

Review guide

Formula sheet provided with the exam.

............................................................................................................

On a cylinder radius a: dA=a dz d(theta)

Reference for surface area defined parametrically

Web resources: Library of Math COW