1
Problem. Blood ow
When uid ows down a pipe not all the particles travel at the same velocity. In laminar ow,
uid particles move along straight parallel paths in layers, called laminae. The velocity in adjacent
layers are not the same. Those in the cente
1
Problem. Battery
We will insist on the importance of units in engineering applications. Dimensions indicated by
numbers depend on the corresponding units: 1 meter = 100 centimeter, but 1 does not equal 100.
The number and the unit are inseparable, at le
1
Problem. (MAE/TAM) The Shape of a Hanging Cable.
The gure below shows part of a exible cable hanging under its own weight (which is w N/m).
The gure also shows a diagram of the forces which, in equilibrium, must add to zero. A exible
cable is one that c
1
Problem. Derivatives re-visited
In engineering and scientic problems, the data are often noisy: even if the tabulated function
f (x) is supposed to be nice and smooth, errors in measurement and computation might affect
the result. Often the errors in me
1
Problem. Lake
A round lake of diameter d is fed by a river and drained by seepage. The normal ow rate of the
river is Qin = 40 m3 /min and is equal to the rate of seepage. Thus, the water level in the lake is
constant. Should the lake level rise, the wa
1
Problem. Skydiving
Were told that feathers and cannonballs fall at the same rate in a vacuum, but in this problem we
calculate that not all skydivers fall at the same rate in air. Youll need to review section 7.8 that tells
how the tanh function is dene
1
Problem. Rocket Path Length
(AEP) The simplest model for the ight of a scientic sounding rocket is that of a non-rotating, at
earth with no atmosphere. Using this model, we wish to determine the total path length of the
trajectory for heights above 72 k
Math 1920
Group Work Problems
13 Sep 2012
1. Give an example of a line with two parametrizations r1 (t) and r2 (t) for which there is
no t such that r1 (t) = r2 (t).
Answer: Let r1 (t) = t and r2 (t) = t+1. t = t+1 has no solution. Keep in mind
that if tw
Math 1920
Group Work Problems
11 Oct 2012
Very Basic Problems: If you get stuck on these, you need to review immediately.
1. In the following, there will be a function f (x, y) and an equation g(x, y) = 0, and you
are asked to nd the maximum and minimum v
Math 1920
Group Work Problems
30 Oct 2012
1. Let f (x, y, z) = x + yz, and let C be the line segment from P = (0, 0, 0) to Q = (6, 2, 2).
a) Calculate f (c(t) and ds = c (t) dt for the parametrization c(t) = (6t, 2t, 2t) for
0 t 1.
b) Evaluate
C
f (x, y,
Math 1920
Group Work Problems
25 Oct 2012
1. Use spherical coordinates to compute the integral of over the region x2 + y 2 + z 2 4,
z 1, x 0. Draw a picture of the domain rst!
Answer: See 23 Oct solutions.
2. Find the volume of the [axisymmetric] region d