Some Useful Math
Definition of the number e. The series expansion of ex. Solving the differential equation dy/dx = ay.
The Natural Logarithm.
Real numbers as vectors. The square root of -1. Polar Coordinates in the plane.
An elementary discussion of various exponential integrals that arise in understanding Maxwell's velocity distribution in the kinetic theory of gases.
How far from the start can you expect to get in a series of equal steps in a straight line, when each step is forward or backward depending on the flip of a coin? This problem is central to statistical physics: its solution is the key to diffusion, conduction and fluctuations in nanosystems.