### New this year! Laptop lending program (Details)

### Syllabus for Spring, '07:

Instructor: Mr. Sullivan
Email: sullivan@kenyon.edu

Office: RBH 206 Phone: 427-5830

Lecture/Lab: TTh 9:40-11:00AM (period B) Classroom: FSH 205

Office Hours: MWF 10:10-11:00 and WF 11:10-12:00N (or by
appointment)

*Dynamical Systems in
Scientific Computing* focuses on using computers to simulate natural
phenomena. This has become vital part of scientific inquiry in many fields and
this course will draw examples from several disciplines, not just physics. One
of the reasons that computer simulation has become so important is the discovery
that many even very simple systems are not solvable with analytical mathematics
*even in principle*. Another reason is
that the advances in computing power has made more and more realistic
simulations possible. We will learn about using the computer to solve ordinary
differential equations with an examples of radioactive decay and space flight,
iterative maps using an example from population dynamics in biology,
percolation problems using a model of a forest fire, and (hopefully) partial
differential equations from electromagnetism.

A subtext of the course is to increase your programming
skill. The prerequisite is an introductory course in programming like Math 118,
or equivalent experience in some procedural programming language like C++,
Java, or FORTRAN. Some of the programming you will be doing will be in C++ or C
and some in a higher level language called IDL which you will be introduced to
during the class. There will be *six*
programming exercises during the semester combined with exercises designed to use the programs
that you have written to discover something about the physical systems modeled.
Each assignment will receive a letter grade. The final grade for the semester
will simply be the average of the grades on each assignment. There will be no
quizzes or exams. I have an absolute grading scale, so you are never in
competition with other students in the class. So, I encourage you to cooperate
and discuss the assignments. However, what you turn in to me must be your own
work, never just a copy of a community solution.

There is no required text for the course. However, students
are strongly urged to retain and use their text from their C++ class. Also, I
strongly recommend that you purchase the book “An Introduction to Programming
with IDL” by Kenneth Bowman which I have found to be the best IDL text of the
ones I have examined so far. A bonus to buying the book is a coupon in the back
to obtain IDL for your own computer for about $50. For those who get really
interested in scientific computing, I also recommend that you obtain a copy of
“Numerical Recipes in C” by Press, et al. This is a great introduction to the
most often used numerical techniques in scientific computing. Attendance is not
graded, but the lack of a text makes excellent attendance nearly mandatory in
practical terms.

I am committed to making it possible for everyone to be
successful in this course and I will enjoy getting to know each of you a little
better. Please make good use of my office hours. Ask lots of questions when I
am unclear in class. If there is something hindering your success in the course,
please come talk to me in private. Potential problems might be aspects of the
course I can change, problems with other students, or learning disabilities. In
the latter case, you are urged to consult with Erin Salva (salvae@kenyon.edu, 427-5453) in the Office
of the Dean of Academic Advising.

### Assignments:

In this assignment you will explore the decay chains that lead to the
stable isotopes of lead. These can be used to date the formation of the
solar system and provide a lower bound on the age of the Universe. From
a computational point of view, you will be learning about and
implementing several techniques for integrating ordinary differential
equations (ODEs). You will start to discover why the technique chosen
matters to you.

This assignment continues our exploration of numerical solutions
of ODEs. Here the context is oscillating systems, first mechanical (the
simple pendulum) then nonlinear chemical oscillators that can become
chaotic oscillators. We will see how geometry can be used to
characterize chaotic oscillations.

In this exercise, you will construct a simulation of the ill-fated
Apollo 13 mission. The moon landing was aborted when there was an
explosion in an oxygen tank. The crew spent a harrowing couple of days
in an orbit that had them loop around the Moon while they tried
everything to conserve heat and electricity. Fortunately, the mission
ended well. Here you will learn about letting others help you to
program by learning about the higher level language

IDL.

Here we have a change of pace. We model a forest fire as a discrete dynamical system called a

cellular automata. Using this system we learn some surpising results of a class of models called

pecolation models.

In this assignment we introduce the solution of partial differential
equations (PDEs) in the context of heat diffusing along a bar of
material. We continue use of

IDL and expand our use of its graphical and animation capabilities.

#### Assignment #6: Individual Projects

Your final assignment is to take one of the previous assignments and
expand upon it in some way. You can expand upon it either by getting
deeper into the science of the model or by going further in
computational techniques. You get to choose your project, though you
must present a one paragraph proposal describing your project for my
approval. Beware of taking on too much!