Study Guide

Points, Vectors, and Functions

Points, Vectors, and Functions Introduction

If calculus seems as intimidating as a bear standing on its haunches considering which part of you to eat first, you aren't alone. The biggest key to tackling this beast is understanding the tools mathematicians, scientists, and engineers use in their endeavors with calculus; the most important concepts are functions, points, and vectors. With these tools, we won't need to run or possibly suffer an untimely demise. Instead, we'll be able to stand tall and tame the calculus bear.

Depending on your previous math classes, you may or may not have seen these tools before. Depending on your memory, you may or may not remember them if you have (we find that most people have to see a math idea two or three or four times before it sticks). Either way, we want to make sure it sticks this time, so we won't leave you stranded in the woods, fearful for your safety.

The goodies in this section include:

  • A zoo of different species of functions and some useful words for describing them. If you make friends with them, they might help you fight off the bear.
      
  • More interesting kinds of functions. With the help of vectors, functions are no longer restricted to taking one number in and putting one number out, now functions can take in and put out multiple numbers. If you don't like them, these exotic creatures might make tasty bear feed.
      
  • Parametric, vector, and polar functions, which are all sort of the same thing. It's kind of like talking to a multilingual parrot: he'll repeat what you say to him in different ways.

Points, Vectors, and Functions Resources

Websites

Math is Fun: Increasing and Decreasing
Functions can be complicated sometimes. If you're still having trouble figuring out which way is up, this link will help you. It should help you figure out which way is down, too.

Math is Fun: Even and Odd Functions
This is a little extra help on how to check if a function is even or odd. You won't be able to tell how many legs a function has. That's in the next chapter.

Math is Fun: Polar and Rectangular Coordinates
No, we aren't talking about bears and squares. These two different coordinate systems are two different ways to describe the same thing, and they are explained briefly in this link.

Videos

Meat-A-Morphosis: An Introduction to Functions
Someone once said that a way to a man's heart is through his stomach. Here's a fun video about food machines, function machines, and steak fries.

Khan Academy: Parametric Equations
See Dick. See Dick drive. See Dick drive over a cliff. Parameterize Dick's fall and untimely demise.

Khan Academy: Rectangular and Polar Coordinates Cartesian to Polar
Need some more help figuring out how to fit a square peg into a round hole? What if you need to fit a round peg into a square hole? These videos explain better how to transform from rectangular to polar and polar to rectangular coordinates.

Khan Academy: Rectangular and Polar Coordinates Polar to Cartesian
Need some more help figuring out how to fit a square peg into a round hole? What if you need to fit a round peg into a square hole? These videos explain better how to transform from rectangular to polar and polar to rectangular coordinates.

Games and Tools

The Function Machine
Still having trouble with functions? Figure out what function is inside the box. It's sort of like Christmas, but you won't be getting a new pair of jeans from the function machine.

Vector Addition and Subtraction
They used to tell jokes and juggle. Now unemployed and in need of juggling equipment, this jester needs your help clearing a path to his ball by adding the vectors tip to tail.

Vector Calculators
If you are still having some trouble, or if you want a calculator to check your answers, here's a tool to help you do basic vector operations. With this, you can rule the world.

The Engineering Toolbox: Polar Coordinates Converter
Here's a link on how to convert between polar and rectangular coordinates. It has a calculator, to boot!

A Parametric Polar Plotter
Plot your own polar functions, and waste hours online making neat polar art. This link will also help you learn how to choose bounds on θ to stop your polar function and your head spinning.