Physics 115/242, Computational Physics
Instructor: Peter Young, ISB, 212
Time and Place: MW 4:00-5:45 pm, ISB 231
Office Hour: Fridays 10:00-12:00.
Note:
This course assumes that you can write a
simple program in one of the following languages: C, C++, Java, or Fortran.
If you are not sure whether you have sufficient fluency in programming,
please see me.
The second half of the course will use Mathematica. No
previous experience of this is required, since the basics will be discussed in
the lectures and a 50 page introduction
has been written for the class (which is available
below).
You will also need
a knowledge of classical and quantum mechanics, and statistical mechanics
at the undergraduate level.
Please email me at
if you have any
questions about necessary prior experience.
I have prepared a considerable amount of material for this class, which will
be available on this web site.
Students' performance will be evaluated from homework assignments and projects,
and a take
home final examination.
Note:
To access homework solutions you need a user name a password. The username is 115.
The password will be announced in class.
Table of contents:
-
Course Description
-
Homework:
-
Exams:
-
Handouts:
-
Representation of numbers on the computer
[pdf]
-
Mathematical equivalence does not mean
computational equivalence
[pdf]
-
Numerical Differentiation: Approximation and Roundoff Errors
[pdf]
-
Romberg Integration
[pdf]
-
Slowing down of the rate of convergence in numerical
integration due to
a singularity at the boundary of the region of
integration (and how to avoid this)
[pdf]
-
Numerical results for some root finding algorithms
[pdf]
-
Comparison of methods for integrating the simple harmonic
oscillator
[pdf]
-
Leapfrog (Verlet) and other "symplectic" methods for
integrating Newton's equations of motion
[pdf]
-
The FPU problem
(a talk by David Campbell)
-
The Kepler problem
[pdf]
-
Sorting routines
[pdf]
-
Least squares fitting
[pdf]
-
Approach to the central limit theorem
[pdf]
-
Randu: a bad random number generator
[pdf]
-
Estimating the error bar from the data
[pdf]
-
How to use the C built-in random number generator rand():
randomnos.c
-
A simple random number generator in C:
testrandpy.c
-
Monte Carlo simulations in Statistical Physics
[pdf]
-
Introduction to Mathematica
[pdf]
-
The zeroes of the Riemann zeta function
[nb]
[pdf]
-
Range of a projectile including air resistance
[nb]
[pdf]
-
Logistic Map (period doubling route to chaos)
[nb] (large)
[pdf].
High resolution image
[pdf].
-
The Sine Map
[nb]
[pdf]
-
The Duffing equation (transition to chaos in a differential
equation)
[nb] (huge)
[pdf]
-
The Sierpinski gasket (a fractal)
[nb]
[pdf]
-
Fractals from the Newton-Raphson method
[nb] (very large)
[pdf]
-
The Mandelbrot set (an example of a fractal)
[nb] (humongous)
[pdf] (very large)
-
My favorite YouTube video of the Mandelbrot set (it can be viewed in high
definition):
http://www.youtube.com/watch?v=9G6uO7ZHtK8
-
Quantum wells - Eigenvalues of the Schrödinger equation for a
rectangular well
[nb]
[pdf]
-
Quantum wells - Eigenvalues of the Schrödinger equation for a
sech2 well
[nb]
[pdf]
-
The shooting method applied to the energy levels of the
simple harmonic oscillator and other problems
[nb]
[pdf]
-
Energy levels of the anharmonic oscillator using
matrix methods
[nb]
[pdf]
Peter Young's Home Page
Last modified:
Fri May 27 10:27:39 PDT 2011