Before you read this, I suggest you read post 19.10. Foxes eat other animals (they are predators), including rabbits: rabbits are eaten by other animals (they are prey), including foxes, but rabbits eat only plants. Now let’s imagine an island that contains foxes and rabbits; there are no other animals for the foxes to eat… Continue reading 22.17 Model for a simple ecosystem – coupled differential equations

This post is about an obscure mathematical technique that will not interest many people. So why have I written it? There are two reasons. One: I mentioned this topic in appendix 2 of post 22.15 so some readers may want to know more about it. Two: many books on physics and engineering change the mapping… Continue reading 22.16 Jacobians – changing the mapping of an integral

Before you read this, I suggest you read post 22.4. The electrons in an atom can scatter x-rays because they move up and down as the electric vector of the x-rays oscillates, as describe in post 22.4. So, the moving electron is a simple harmonic oscillator if the x-ray wave is a sine wave. The… Continue reading 22.15 X-ray scattering by an atom