I adjust to the needs of the student.

I start with a problem of some sort. For example, calculate the transmission light through a thin film.

1. Discuss the physics of what governs light transmission. Maxwell's equations. What do they mean? Where do they come from?

2. Analysis Light impinges perpendicularly to the film. In this case Maxwell's equations reduce to the one-dimensional wave equation. What is the wave equation? Where does it come from? Do you know that you can derive special relativity from the wave equation? (I discuss this with advanced students).

We can solve the 1-D wave equation analytically. I'll show you how.
Depending on the thickness and index of refraction (what is the index of refraction?) you can design an anti-reflection coating.

Next let's write a finite difference time domain (FDTD) program in Python to solve the wave equation, and we will simulate and visualize the propagation of the light waves in time. We will discuss numerical stability of finite difference equations and how to ensure high accuracy and numerical stability. Compare the output of the computer simulation with the analytical solution.

After that we'll go to two and three dimensions, and write Python programs with visualizations.

I approach this problem step by step, and tailor the content and level to the individual student.

Other Subjects:
Quantum computing
- What is quantum superpostion?
- What is quantum entanglement (and what is not)?
- What is a quantum gate?
- What are the challenges and limitations of quantum computing?

Machine learning
- Bayesian data analysis

For more advanced topics see my book and other opublications: