| Date |
Topic |
Hint |
Quiz 1 : Fri Sep 2
(SOLUTION) |
Functions |
If a mathematical statement is to be proved true, it
must be true in all cases. If it is false, it just has to be shown false for
one case. |
Quiz 2: Fri Sep 9
(SOLUTION) |
Population Model |
What kind of function is very closely related to its
own derivative? |
BONUS Quiz 1 : Fri Sep 9
(SOLUTION) |
Models and Euler |
Factor carefully! |
BONUS Quiz 2 : Fri Sep 16
(SOLUTION)
|
Euler's Method and
Slope Fields |
To find the equations of the lines in (c) you
already have all the numbers you need from your answers in part (a). |
Quiz 3: Mon Sep 19/ Tue Sep 20
(SOLUTION) |
Euler's Method and a
System of IVPs |
|
BONUS Quiz 3 : Fri Sep 23
(SOLUTION)
|
Explaining S-I-R |
Think carefully about the number of people being
infected per day. This is NOT the same thing as the rate of change of the
infected population with respect to time, i.e. I'. |
Quiz 4: Mon Oct 3/ Tue Oct 4
(SOLUTION) |
Limits and Continuity |
|
Quiz 5: Fri Oct 7
(SOLUTION) |
Derivatives |
HINT: Recall the limit definition for the derivative
f'(x) of a function f(x). Does the definition depend on how scary the function
f(x) is? |
Quiz 6: Fri Oct 14
(SOLUTION) |
Rules of Differentiation |
HINT: Carefully consider what is the inner and outer
function for f(x) and g(x), specifically thinking about how the input variable
is acted on to produce an output. |
BONUS Quiz 4: Fri Oct 14
(SOLUTION) |
Relative Rates |
HINT: This related rates problem is really just an
implicit differentiation problem. |
BONUS Quiz 5: Wed Oct 19
(SOLUTION) |
Inverse Functions |
HINT: If you don't use the HINT in part (e) then
you'll have to use the chain rule. |
Quiz 7: Mon Oct 31/ Tue Nov 1
(SOLUTION) |
Indeterminate Forms |
|
Quiz 8:
Fri Nov 4
(SOLUTION) |
Equilibrium Values and
IVPs |
HINT: Think about the special values we
consider when we have graphed population behavior. |
BONUS Quiz 6:
Fri Nov 4
(SOLUTION) |
More IVP Solutions |
HINT: If you have a solution in implicit form, its
derivative can be implicitly found as well. |
Quiz 9:
Fri Nov 11
(SOLUTION) |
Qualitative Analysis of
Rate Equations |
HINT: Recall what information the SIGN
of y' and the SIGN of y'' give you about the shape
and direction of y(t). |
Quiz 10:
Mon Nov 14
(SOLUTION) |
Higher Order Taylor
Polynomials |
. |
Quiz 11:
Fri Nov 18
(SOLUTION) |
Optimization |
HINT: Recall, that for a statement to be true
it must be true in EVERY case described. A statement is false, if it is
false just once. |
Quiz 12:
Wed Nov 30
(SOLUTION)
Due Mon Dec 5. |
Partial Derivatives and
Multivariable Optimization |
HINT: Recall, for a product AB=0 either A=0
or B=0 or both. Also, a global extreme value of a function means
that either there is a largest(smallest) possible output value regardless of
input value. |