Exam #2
The exam (May 5, 2:45 pm)
will test you on concepts developed in lecture and
techniques used in homeworks, labs, and projects.
The material covered will be mostly since the lecture of March 4,
though many of the techniques we used in the second half of the
course were introduced in the first half (still need to know
some Mathematica, for example.) As in the first exam,
be prepared to answer questions about key mathematical and
physical results, to write pseudo-code algorithms for problems
resembling those in homework and labs, and to write a few
syntactically correct lines
of C and Mathematica.
You will not be asked to write JavaScript yourself, but you may
be asked to describe what a given script does based on your knowledge
of JavaScript. [Sample JavaScripts covered in
lab are located at www.phy.syr.edu/~phy307/jscript]
Things to know, in more detail
- Dynamical systems and chaos
- What are Poincare sections and how are they used to classify
dynamics? How are Fourier transforms used to classify the temporal
behavior of a system?
- What are bifurcation diagrams?
- How is the Lyapunov exponent defined and how is it related to
the concept of "sensitivity to initial conditions"?
- How can one
estimate the Lyapunov exponent numerically (using simulations)?
- What is the difference between equations of motion and
maps? What is their relationship and how are maps used to study
dynamical systems?
- What are iterated maps used for (how are they related
to period doubling, for example?)
- What is spatio-temporal chaos? What are examples of chaos
in experimental systems (review reading in the book)?
- Fractals
- What is a "fractal"? What is the geometric concept of
self-similarity? Know how to calculate the dimension of
simple fractals (not numerically, but exactly.)
- How does one numerically calculate the dimension of a fractal?
- How do fractals arise in the study of dynamical systems?
- Partial Differential equations
- What is the partial differential equation for
diffusion in its simplest form?
- What is the finite difference method used to solve the
diffusion equation (in one and two dimensions)? How is this
method implemented in C code (with and without periodic boundary
conditions.)
- What is the implicit method for solving the diffusion
equation?
- What is a reaction-diffusion equation and how is it related
to models of morphogenesis and chemical reactions?
- Mathematica
- Know the material used in the first exam.
- Review how NestList[] was used to generate orbits
for maps.
- Know how to define functions, for example, on two-element lists
(as used in two dimensional maps.)
- Review how to calculate Lyapunov exponents using Mathematica.
-
- C
- We did not introduce many new language elements in the second
half of the course; review your knowledge of C that might be used
to write simple portions of code on the exam.
- JavaScript
- Understand how JavaScript is used to liven up HTML documents.
- Review how the flip and clock scripts work, in particular.