Syllabus

Overview of the computational physics topics in this course-style note cluster.

Core theme

The course is about turning physical models into numerical experiments. Instead of only solving equations analytically, we approximate them on a computer and check how the approximation behaves.

Main topic list

• Linear and nonlinear differential equations.
• Numerical integrators for time evolution.
• Monte Carlo methods and numerical simulations.
• Radioactive decay as a first stochastic / exponential-decay model.
• Ballistic motion with numerical integration.
• Harmonic motion and the simple harmonic oscillator.
• Pendulum motion as the first easy nonlinear-ish oscillator example.
• Chaos and sensitivity to initial conditions.
• Root finding and numerical integration/quadrature.
• Random walks and diffusion-like behaviour.
• Cluster growth and percolation.
• Ising model and phase transitions.

First problem vibe

The first problem should be a gentle simple harmonic oscillator / pendulum task:

$$\ddot{x}+{\omega }^{2}x=0$$

or, for a pendulum without the small-angle approximation,

$$\ddot{\theta }+\frac{g}{L}\sin \theta =0.$$

Good early checks:

• Does the numerical solution conserve energy when it should?
• Does the timestep change the answer?
• Does the method remain stable over many oscillations?

Numerical-methods sanity checks

For every simulation, ask:

1. What equation am I solving?
2. What approximation did I introduce?
3. What is the timestep/grid/sample size?
4. What physical quantity should be conserved or trend predictably?
5. How do I know the result is not just numerical nonsense?

Course text

Likely textbook anchor:

Computational Physics

Add exact author/edition when known.

Related

• ASTRO MOC