todo: copy over the intro from the KLMC2 superposition notebook
but yeah the cond and the negative cond are like attractive and repulsive forces
what are some of the benefits of modeling things as potentials?
- Laplace Operator as a measure of local curvature
- Green’s Functions as a divergence
- Harmonic Functions: Functions that satisfy Laplace’s equation are known as harmonic functions. They have numerous nice properties, including the mean value property, which states that the value of a harmonic function at a point is equal to the average of its values on any sphere centered at that point.
- Heat Equation: The Laplace operator also appears in the heat equation, which describes the distribution of heat (or variation in temperature) in a given region over time: