## Basic Math Tools

## 1. The operator

a. If 'a' is a constant then

b. If a is a constant then

c. Given two series x and y then

d. Given two series then product and division look like

e. Given two series then the double sum operates as

## 2. Properties of linear functions

a. Intercept and slope:

b. Partial effects:

## 3. Proportions and percentages

a. Change

b. Proportionate change

## 4. Special Functions

a. Quadratic functions

b.Natural Logarithms: y = log(x), The graph: Increasing at a decreasing rate.

c. The Exponential: y = exp(x), The graph: Increasing at an increasing rate.

## 5. Differentiation

a. The derivative is a linear operator so its properties are similar to the summation operator.

b. The derivative tells us the rate of change or slope of a function.

b. A rule:

c. When the first derivative is zero then the functino has reached either its maximum or its minimum.

d. Partial differentiation.

e. The chain rule: