|
# |
Date Assigned |
Date Due |
Topic |
Hint |
|
Quiz 1 |
Fri
Sep 10 |
Mon Sep 13 |
Introduction to Differential Equations |
Think about the particular solutions in
u variables, what would the initial conditions be then? |
|
BONUS Quiz 1 |
Fri Sep 17 |
Mon Sep 20 |
Singular Solutions |
A singular solution to a DE is another
solution that does not fit into the family of solutions generated by
changing the constant of integration. |
|
Reading Quiz 1 |
Fri Sep 17 |
Fri Sep 17 |
Section 1.1-1.4 |
|
|
Quiz 2 |
Fri Sep 24 |
Mon Sep 27 |
Bifurcations |
HINT: when sketching the bifurcation
diagram, think about whether there is any value of alpha which would
correspond to zero as an equilibrium value. |
|
Reading Quiz 2 |
Wed Oct 6 |
Wed Oct 6 |
Section 1.5-1.9 |
|
|
Quiz 3 |
Fri Oct 8 |
Mon Oct 11 |
Systems of Differential Equations |
HINT: think about how many initial
conditions go along with a 1st order differential equation in order to find
a particular solution, and how that number is related to the number of
unknown constants in the general solution to a 1st order ODE. |
|
Quiz 4 |
Fri Oct 8 |
Mon Oct 11 |
Solving Linear Systems of Differential Equations |
HINT: Recall how you can check whether an
eigenvector is associated with an eigenvalue is if it solves Ax=qx where q
is an eigenvalue and x is eigenvector. |
|
BONUS Quiz 2 |
Fri Oct 29 |
Mon Nov 1 |
Visualizing Solutions of Linear Systems of
ODEs |
HINT: Also draw in the straight-line
solutions. What does existence and uniqueness theorem tell you about
crossing these solutions? Our general solution previously discussed applies
to zero eigenvalues. What is e^0?. |
|
Reading Quiz 3 |
Fri Nov 5 |
Fri Nov 5 |
Section 3.1-3.5,3.7 |
The Reading quiz will not include section
3.6, which is about 2nd Order Linear ODEs. |
|
Quiz 5 |
Fri Nov 12 |
Mon Nov 15 |
Bifurcation in Linear Systems of
ODEs |
HINT: What property of the matrix controls
when a linear system of ODEs will change its character? |
|
Quiz 6 |
Mon Nov 22 |
Mon Nov 29 |
Laplace Transforms |
HINT #1: You basically need to do one step
of integration by parts in order to get the formula for L{t^a}. Think about
which function in the integral you want to differentiate in order to have
t^(a-1) appear.
HINT #2: Try integration by substitution in order to obtain
the definition of Gamma[a] |
|
BONUS QUIZ 3 |
Fri Dec 3 |
Mon Dec 6 |
Advanced Laplace Transforms |
HINT: Notice the difference in where the
two sums start. (i.e. the starting index value). Also, note that anything that doesn't have a
k in it does not
need to be to the right of the summation symbol. The graphs of b(t) and
f(t)=a(t)-b(t)
should be especially pretty. :) |
