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# |
Date Assigned |
Date Due |
Topic |
Hint |
|
Quiz 1 |
Fri
Sep 11 |
Mon Sep 14 |
Introduction to Differential Equations |
Think about the particular solutions in
u variables, what would the initial conditions be then? |
|
BONUS Quiz 1 |
Fri Sep 18 |
Mon Sep 21 |
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 |
Mon Sep 21 |
Mon Sep 21 |
Section 1.1-1.4 |
|
|
Quiz 2 |
Fri Oct 2 |
Mon Oct 5 |
Practice
with 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 |
Mon Oct 12 |
Mon Oct 12 |
Sections 1.5-19.9, 2.1-2.4 |
|
|
Quiz 3 |
Fri Oct
30 |
Mon Nov 2 |
Trajectories
of Solution Curves |
HINT: Although the question does not explicitly
ask you to, you should find the eigenvalues and eigenvectors of the
associated matrix. You can use their signs to determine the stability of the
origin and thus the trajectories of the solutions that start at the given
initial conditions. |
|
BONUS Quiz 2 |
Fri Oct 30 |
Mon Nov 2 |
Visualizing
Linear Systems Solutions
|
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? |
|
Quiz 4 |
Fri Nov 6 |
Mon Nov 9 |
Bifurcations in Linear Systems of
DEs |
HINT: What property of the matrix controls
when a linear system of ODEs will change its character? |
|
Reading
Quiz 3 |
Fri Nov 13 |
Fri
Nov 13 |
Sections 3.1-3.7 |
|
|
Quiz 5 |
Mon Nov
23 |
Mon
Nov 30 |
Introduction to
Laplace Transforms |
HINT: 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 |
Wed Dec 2 |
Mon Dec 7 |
Advanced Laplace Transforms
|
HINT: Notice the difference in where the
two sums start. 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. :) |
|
Reading Quiz 4
|
Fri Dec 4 |
Fri Dec 4 |
Laplace Transforms Summarized |
May be Take Home Quiz instead.
|
