*Definition of the number e. The series expansion of e ^{x}. Solving
the differential equation dy/dx = ay. *

*The Natural Logarithm.*

*Real numbers as vectors. The square root of *-1*.
Polar Coordinates in the plane. The significance of the formula _{}*

*Exercises on Complex Numbers PDF*

**Some
Exponential Integrals PDF**

*An elementary discussion of various exponential integrals that arise in understanding
Maxwell’s velocity distribution in the kinetic theory of gases.*

**The One-Dimensional Random Walk PDF**

*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.*