Physics 115/242, Computational Physics
Instructor: Peter Young, ISB 212,
petery@ucsc.edu
Time and Place: MWF 9:3010:40 pm, ISB 231
Office Hour: Fridays 10:4512:00, and at other times by
appointment.
This course assumes that you can write a
simple program in one of the following languages: C/C++, Java, or Fortran 90.
Homework solutions will be given in C.
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 will be available
below).
You will also need
a knowledge of classical and quantum mechanics, and statistical mechanics
at the undergraduate level.
Please email me at the above address
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.
Table of contents:

More Detailed 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]

RungeKutta code for integrating the simple harmonic oscillator
[rk2_SHO_all.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]

How to use the C builtin random number generator rand():
randomnos.c

A simple random number generator in C:
testrandpy.c

A fairly detailed discussion of data analysis and fitting,
http://arxiv.org/abs/1210.3781

Distribution of the sum of random variables (from 116C)
[pdf]

Proof of the central limit theorem in statistics (from 116C)
[pdf]

Approach to the central limit theorem
[pdf]

Randu: a bad random number generator
[pdf]

Estimating the error bar from the data
[pdf]

Sample code for Monte Carlo integration
[pdf]

Monte Carlo simulations in Statistical Physics
[pdf]

Java applet simulation of the 2d Ising model:
http://young.physics.ucsc.edu/ising/ising.html

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] (very large)
[pdf]

The Sierpinski gasket (a fractal)
[nb]
[pdf]

Fractals from the NewtonRaphson method
[nb] (very large)
[pdf]

The Mandelbrot set (an example of a fractal)
[nb] (humongous)
[pdf]

My favorite YouTube video of the Mandelbrot set (I recommend viewing it in high
definition):
http://www.youtube.com/watch?v=9G6uO7ZHtK8
Another YouTube video zooming in on the Mandelbrot set:
http://www.youtube.com/watch?v=0jGaio87u3A

Quantum wells  Eigenvalues of the Schrödinger equation for a
rectangular well
[nb]
[pdf]

Quantum wells  Eigenvalues of the Schrödinger equation for a
sech^{2} 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]

Solitons in the Kortwegde Vries equation.
[nb]
[pdf]

Photo of a soliton on the Scott Russell Aqueduct in Scotland

Scott Russell's account of his first observation of a "Wave
of Translation" (now called a "soliton") in 1834.

The SineGordon equation.
[nb]
[pdf]
Peter Young's Home Page
Last modified:
Wed Jun 4 14:40:23 PDT 2014