Math 3510 Section 410 Homepage
News & Announcements
05/09 Final grades are posted on AsULearn. For both tests I posted a raw point score,
a percentage, and a corresponding letter grade (as a comment on the percent test
score). I posted a project, presentation, participation grade (the posted score
reflects all of these things put together). Finally, I posted a final course
average. Your letter grade for the class is posted as a comment on the final course
average.
I will leave your final work in an envelope with your name on it in my mailbox
and/or the folder on my door.
If you have any questions about your grade, please email me. If you want to speak
with me in person, we can arrange a time to meet.
If you ever have any questions, mathematical or otherwise, please ask. I'm happy
to help in anyway I can.
Have a great summer!
05/03 ODE Symmetry Slides
04/25 Variation of parameters and linear systems examples (.mw) (.pdf)
04/20 Homework Set #5 suggested due date Thursday, April 24th.
04/19 LaTeX Example Source Files -- a paper, an answer key, some formulas, handouts, and slides.
04/18 As discussed in class today...
(1) We will have our second (and final) test Tuesday, April 30. It will cover all of the
differential equations material we've covered. You may bring in a page of notes
(standard size sheet of notebook or copy paper, front and back is ok). But no technology
may be used while taking the test [no calculator, Maple, etc.]
(2) Final projects: If you haven't talked to me and picked out your project, you need to do
so by TUESDAY. The project paper is due at least 24 hours before the final exam period.
Your project should be at least 5 pages (single spaced) typed up. Make sure you spend a
page or two discussing some background (a bit of history would be nice if it makes sense)
then spend a few pages on main results/theorems/important techniques (whatever makes sense),
and then each person should have at least 5 "homework" problems worked out (a couple of easy
straight forward calculations, a couple middle of the road proofs/derivations/calculations,
and then at least 1 "challenge" problem (something more difficult). For those working in a
group, make sure you turn in some portion of the paper written entirely by yourself (and
marked as such) in addition to your "homework" problems. I would prefer that you use LaTeX,
but Word or Maple or something similar would be ok. I'll post some sample LaTeX source files
soon. We will use the final exam period for presentations. Plan on 5-8 mins to explain your
topic [you'll be teaching the class]. For final presentations, if you'd like to make slides
and use the computer projector, great. If not, a "chalk talk" is ok too.
(3) Homework #3 is DUE TUESDAY.
(4) I will endeavor to post Homework #5 (our final homework) soon.
04/11 Undetermined Coefficients examples (.mw) (.pdf)
04/07 Homework Set #4 suggested due date Tuesday, April 16th.
03/27 SORRY! Problem #4 part (c) is false in every possible way. Just skip it.
(Commuting operators don't have to share eigenvalues or eigenvectors.)
If you've already put a lot of time into it, feel free to include what you've
found and it'll be worth something.
03/21 Two examples of computing the Jordan form and exponential of a matrix as well
as an example of finding the square root of a matrix: Maple worksheet (.mw) (.pdf)
03/20 Test #1 (linear algebra) is due Wednesday, March 27th at 5pm
Thursday, March 28th at 3:30pm.
You may refer to notes, textbooks, and the internet while working on these problems.
If you get an answer from some source (textbook or internet), please cite your source.
For some problems you will want to use Maple (or something equivalent).
Do not discuss these problems with anyone other than me.
03/05 Hey! It helps to actually post a link to the homework...oops!
Homework Set #3 suggested due date Tuesday, March 19th.
03/03 An example of computing the Jordan form of a matrix in Maple: Maple worksheet (.mw) or (.pdf)
02/08 Homework Set #2 suggested due date Thursday, February 14th.
01/24 Homework Set #1 suggested due date Thursday, January 31st.
Please note: If homework webpages don't print well, you
can download a package of fonts to help things look better.
The fonts (and installation instructions) can be found here.
For PCs: PC jsMath fonts and
For Macs: Mac jsMath fonts
01/15 Some old 2240 handouts: (I'll print off copies to hand out in class)
Gauss-Jordan Elimination & The Linear Correspondance
Finding & Extending Bases Example
Coordinate Matrix Example
Kernel, Range, Composition of Linear Transformations Example
Eigenhandout
01/14 The syllabus and tentative schedule have been posted.
This course has been registered with the Maple Adoption Program so that
you can purchase Maple Student Edition at a discounted price. To do so,
visit Maplesoft's web store at https://webstore.maplesoft.com and use
promotion code: AP97261-7D479
01/08 Course Data
MAT 3510 Section 410
JUNIOR HONORS SEMINAR
Meeting Times TR 09:30am-10:45am
Room WA 308
Course Title & Description:
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MAT 3510-410 "Junior Honors Seminar" 3 credits
Prerequisite: 1120 (Calculus I & II), 2240 (Linear Algebra),
& 2110 (Intro. to Proofs)
Title: "Differential Equations from an Algebraic Perspective"
We will spend approximately half of the semester exploring topics
from advanced linear algebra. Then the remainder of the semester
will be devoted to methods for solving differential equations and
systems of differential equations. Although I will assume familiarity
with the basics from linear algebra, I will not assume any background
from differential equations. Some topics may intersect with group or
ring theory (modern algebra), but any background will be covered as
needed.
We will cover the following topics (in more or less detail according
to interest):
Linear Algebra: dual spaces, quotient spaces, Jordan canonical form,
the matrix exponential, tensor products, and exterior
algebras.
Differential Equations: solving DEs by factoring linear operators, the
methods of undetermined coefficients, variation of
parameters, and a partial fraction decomposition
technique for solving non-homogeneous linear DEs, using
the matrix exponential and variation of parameters for
solving systems of DEs, symmetry methods for solving DEs
(finding integrating factors and very basic, very applied
Lie theory), and (if there is interest), some differential
algebra which would including a touch of differential
Galois theory which attempts to answer the question, "When
can we solve a differential equation?"
Note: Although having courses in modern algebra or differential equations
would be helpful, I will *not* be assuming that anyone has this
background! Any DEs or modern algebra background will be covered in
class as needed.
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Syllabus and schedule pages
will be posted later...
Any questions about this class?
Send me an email at cookwj@appstate.edu
Term Project Ideas: More suggestions later...or come up with one of your own!
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- Show the dimension of the dual space is strictly larger (in cardnality)
for infinite dimensional vector spaces.
- A deep look at Wronskians (how do they behave when your functions are
not solutions of linear DEs?) and Abel's theorem.
- Linear difference (not differential) equations (recurrence relations) -- a
discrete variant of the theory we will being looking at.
- Lie algebras (lots of potential projects here)
- Manifolds & Lie groups (especially as they relate to solving DEs).
- Hurwitz's theorem, Octonions, weird algebras
- Differential forms (extending exterior algebra) and/or DeRham cohomology.
- Group representation theory/character theory.
- Jacobson's density theorem.
- Other canonical forms for matrices (such as rational canonical form).