**Some Quick and Dirty Mathematical References**

**"**Do not worry about your difficulties in mathematics, I assure you that mine are greater**"** - Albert Einstein ( 1879 - 1955 )

**Square Roots of Negatives**

**Some Quick and Dirty Relativity Approximations**

**I**

**III**

**Integration By Parts**

**Natural Logarithm, ln x**

**§ Some implications for natural logs:**

**The Inverse of ln x and the number e**

**§ Definition of number e:**

**§ Number e defined numerically:**

**§ Properties of ln x and e:**

**§ Laws of exponents for e ^{x}:**

**The calculus for ln x and e ^{x}**

**The Hyperbolic Function**

Every function that is defined on an interval centered at the origin is comprised of even and odd components as follows:

The importance of this class of functions lies in the fact that they best describe the hanging catenary shapes of electrical powerline cables, wave motion in certain elastic solids, and are involved in the differential equations for heat transfer in metals, as well as demonstrating time and distance dilations in special relativity mathematics.

**§ Derived hyperbolic identities:**

**§ The derivatives for these hyperbolic functions:**

**Maclaurin Series for Some Trig Functions**

**§ Small trignometric approximations:**

**§ Maclaurin Series and hence Binomial Expansion vital in deriving :**

**Definitions from Geometry and Rotational Kinematics**

**Spherical Coordinates**

**Unit Circle: Radian Measure**