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Some Useful Math

The Exponential Function   PDF

Definition of the number e.  The series expansion of ex.  Solving the differential equation dy/dx = ay.  

The Natural Logarithm.

Complex Numbers   PDF

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.

 

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