|
# |
Date Assigned |
Date Due |
Topic |
Hint |
|
BONUS QUIZ 4 |
Fri
Nov 15 |
Mon
Nov 18 |
Bifurcations in
Quasi-Linear Systems of ODEs |
HINT: Notice that you don't have t -> infinity in part (d).
Your expression for r(t) in both (c) and (d) should have an unknown constant
C in it.
NOTE: the contradiction between part (a)
saying the system has acenter for all values of a when in actuality
the nature of the fixed point is very different for different values of a!
(i.e. Linearization doesn't work well when the Jacobian has fully complex
eigenvalues or a zero eigenvalue) |
|
QUIZ 8 |
Fri
Nov 15 |
Mon
Nov 18 |
Quiz 8 |
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 (i.e. u=st) in order to obtain
the definition of Gamma[a] |
|
READING QUIZ 3 |
Fri
Nov 8 |
Fri
Nov 8 |
Reading
Quiz 3 |
Covering Sections 3.1, 3.2, 3.3, 3.4, 3.5 and 3.7 of
Blanchard, Devaney & Hall. |
|
BONUS QUIZ 3 |
Fri
Nov 1 |
Mon
Nov 4 |
Visualizing 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?. |
|
QUIZ 7 |
Fri
Nov 1 |
Mon
Nov 4 |
Bifurcations in Planar Systems of ODEs |
HINT: What property of the matrix controls
when a linear system of ODEs will change its character? |
|
QUIZ 6 |
Wed
Oct 23 |
Mon
Oct 28 |
Planar Systems of ODEs |
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. |
|
QUIZ 5 |
Fri
Oct 11 |
Wed
Oct 16 |
Chapter 2 |
Think about what pictures we have seen that represent
equilibrium solutions of ODEs. |
|
READING QUIZ 2 |
Wed
Oct 9 |
Wed
Oct 9 |
Reading
Quiz 2 |
Covering Sections 1.5, 1.6, 1.7,1.8 and 1.9 of
Blanchard, Devaney & Hall. |
|
Quiz 4 |
Fri
Oct 4 |
Mon
Oct 7 |
First Order Linear Differential Equations |
HINT: Closed form means that you don't have an integral in the expression.
Make sure you fill out the Reality Check to get 1 point! |
|
Quiz 3 |
Fri
Sep 27 |
Mon
Sep 30 |
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.
(That tells you were your bifurcation curve crosses the parameter axis) |
|
Quiz 2
|
Fri
Sep 20 |
Wed
Sep 25 |
Qualitative Analysis of the Logistic Equation |
If y'=f(y) where y is a function of t.
Using the chain rule tells you that y''=f'(y)y'(t) |
|
READING QUIZ 1 |
Wed
Sep 18 |
Wed
Sep 18 |
Reading
Quiz 1 |
Covering Sections 1.1, 1.2, 1.3, 1.4 of
Blanchard, Devaney & Hall. |
|
BONUS Quiz 2 |
Mon
Sep 9 |
Mon Sep 16 |
Practice with Separation of Variables |
What are the conditions on f(x,y) the
Existence and Uniqueness Theorem that guarantee a unique solution exists? |
|
Quiz 1 |
Fri
Sep 6 |
Mon Sep 9 |
Introduction to Differential Equations |
Think about the particular solutions in
u variables, what would the initial conditions be then? |
|
BONUS Quiz 1 |
Fri Sep 6 |
Mon Sep 9 |
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. |
