February 14, 2012 --- Class 11 --- Final Project, Higher Order Algorithms,
Introduction to Mathematica
Activities:
Homework
I discussed what I was looking for on the homework and
some of the challenges in the second problem. In general,
performance on the homework was excellent. If you have any
questions, please come to see me. It is important to master
the skills required to solve these initial problems.
Final Project
It is time to start thinking about your final project. Some
of you may have a problem related to your research that can
be used for the project. If not, there may be some problem
that interests you that would serve as a project. If you
don't have an idea of your own, you might like to look through
our text book. If there is a chapter that we will not cover,
you might find some homework problems that can be combined to
make a project. The book also has some suggestions for
projects. Some of these, even in chapters will will cover some
of may make suitable projects. So start to think about what
you want to do, because in a couple of weeks, I will be asking
everyone to get their project approved by me.
Here is how the final project will be graded:
Statement 10
Eq Solved 5
Num. Method 5
Code 5
Results 10
Discussion 10
Critique 5
------------------
Total 50
Higher order algorithms
We talked about several algorithms including leap frog
Adams-Bashforth and Runge-Kutta. Euler-Richardson is
basically the 2nd order Runge-Kutta algorithm. We also
talked about the 4th order Runge-Kutta algorithm. Many of
these algorithms are presented in Appendix 3A of Chapter 3.,
starting on page 74. There are two typos in the book regarding
the 4th order R-K algorithm. In Eq. (3.61g), the right-hand-
side should be multiplied by Delta t. In Eq. (3.61h), k_3x
on the RHS should be k_3v. Corrections to the textbook can
be found at http://sip.clarku.edu/3e/updates.html .
You may also find more about these algorithms in "Numerical
Analysis" by Burden and Faires, or "Numerical Recipes" by
Press et al.
My notes can be found at
http://www.physics.indiana.edu/~sg/p609/ode_algorithms.pdf
Introduction to Mathematica
An eight page handout on Mathematica is available as
~sg/mathematica_notes_sg.pdf
Over the next several classes we will go through the notes
and the examples it contains.
There is a wide variation among class members' familiarity
with Mathematica. Before the next class, please make sure
you understand all of the material in Secs. A-E. In our next
class we will begin discussing random walks.