Calcaus

This chapter reviews the most important things you need to know to start learning calculus.
It also introduces the use of a graphing utility as a tool to investigate mathematical
ideas, to support analytic work, and to solve problems with numerical and graphical methods.
The emphasis is on functions and graphs, the main building blocks of calculus.
Functions and parametric equations are the major tools for describing the real world in
mathematical terms, from temperature variations to planetary motions, from brain waves
to business cycles, and from heartbeat patterns to population growth. Many functions
have particular importance because of the behavior they describe. Trigonometric functions
describe cyclic, repetitive activity; exponential, logarithmic, and logistic functions
describe growth and decay; and polynomial functions can approximate these and most
other functions.
Increments
One reason calculus has proved to be so useful is that it is the right mathematics for relating
the rate of change of a quantity to the graph of the quantity. Explaining that relationship
is one goal of this book. It all begins with the slopes of lines.
When a particle in the plane moves from one point to another, the net changes or
increments in its coordinates are found by subtracting the coordinates of its starting point
from the coordinates of its stopping point.