Homework
due 04_03
04_10 04_18 04_24 05_01 05_08 05_16
05_22
Tutoring for H263 is
held in Cockins Hall, Room 137:
Monday
3:30 – 4:30
Tuesday
11:30 – 3:30
Wednesday
11:30 – 12:30
Thursday
11:30 – 3:30
Final
exam: Mon, June 5
9:30 AM - 11:18 AM (see
the schedule)
Solving all
the homework problems is due every day after class.
The write-ups are due Wednesday
May 31.
Five problems will be graded (2 points each).
Tuesday May 23
Solve, write up and turn in:
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)
Solve (do not turn in): Example 4 p. 777:
calculate the flux using a surface integral.
Wednesday May 24
Solve, write up and turn in:
21.4: 1a,e 3, 5, 7, 9, 13
Thursday May 25
Solve, write up and turn in:
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).
Friday May 26
Solve, write up and turn in:
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.
Tuesday May 30
Solve, write up and turn in:
21.5: 4, 5, 6, 7, 9
Wednesday May 31
Solve:
21.5: 1, 11
Review Chapter 21.
Final
exam: Mon, June 5
9:30 AM - 11:18 AM (see
the schedule)
Review guide
Formula sheet
provided with the exam.
............................................................................................................
For future reference - some formulas for dA that we have
obtained:
On a cylinder radius a: dA=a dz d(theta)
On a sphere raius a: dA=a^2 d(phi) d(theta).
Reference
for surface area defined parametrically
Web resources: Library
of Math COW