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Scientific Computing

This is the web site for PHY 125 Scientific Computing (unofficially known as the Flying Circus). It is a continuation of Informatik für Physikstudierende. We will use Python and its scientific and graphics libraries, introduced in the earlier module, to do some interesting physics problems.

Course Script


Announcements

2012-02-28 – Week 2 exercises: 1.2 (raphson.py) and 1.3 (curlicues.py)
2012-02-28 – Week 3 reading: Please try and read through section 1.6 (Machin's formula) ahead of the next lecture.
2012-03-06 – Week 3 exercises: machin.py, eratosthenes.py, carmichael.py
2012-03-08 – Week 4 reading: Please read chapter 2 until the end of 2.1 (Euler and Runge-Kutta integrators).
2012-03-13 – Week 4 exercises: solvers.py, coffee.py, schiefer_wurf.py, populations.py
2012-03-13 – Week 4 additional material: We have to additional files for you. wurf.py contains the example implementation of Schiefer Wurf discussed in the lecture. affe.py is an optional assignemnt that turns your exercises into a simple game.
2012-03-27 – Week 6 exercise: pendel.py
2012-04-03 – Week 7 exercise: cyclotron.py
2012-04-04 – Week 7 example: odeint_beispiel.py, on how to pass additional arguments with odeint.
2012-04-17 – Week 8 exercise: stromkreis.py
2012-04-24 – Week 9 exercise: daylight.py
2012-05-08 – Week 10 exercise: eigenv.py
2012-05-15 – Week 11 exercise: fourier.py
2012-05-15 – Week 11 additional: sunspots.txt, tahiti.txt, soi.txt


Summary

This course is about physics problems that cannot be solved with brains, pen and paper only, but can be solved if some computer is programming is added. (Though on the way we will digress into problems that are not physics, and we won't always need a computer.) The programs themselves will be fairly simple. The main challenge will be in formulating physics problems in computational terms.

The material is divided into five chapters, as follows.

1. Arithmetic

  1. Finite precision and the generalized Y2K problem.
  2. Root finding and square roots.
  3. Continued fractions and curlicues.
  4. The sieve of Eratosthenes and the distribution of primes.
  5. A thousand digits of π using Machin's formula.

2. Dynamical systems

  1. A predator-prey (Lotka-Volterra) system.
  2. A driven pendulum.
  3. Particle in a cyclotron.
  4. The restricted three-body problem.
  5. Particle near a black hole.
  6. The Friedmann equation and why people are talking about it.

3. Matrix systems

  1. Circuit equations and the resistor-cube problem.
  2. Rotation matrices and daylight over the Earth.
  3. Eigensystems and the time-independent Schrödinger equation.
  4. Fourier transforms and the central limit theorem.
  5. The time-dependent Schrödinger equation.

Books and websites