calculus
Calculus
The Math pages will contain only my study cards until I have sufficient time to devote to these pages.
Any thing that I say on this page can and has been said better at Karls website. If you are in Calc and need some help GO THERE and bookmark his page. It is far superior to anything you will find in my calculus section.
Limits
Differentiation
Differentiation gives you the slope of a function at any point along that functions curve. It's sounds useless for the most part, but trust me it's not.
For example in physics if you have a function that tells you the position of an object [ anything like: x( t ) = x ] then the first derivative will give you a function that tells you the Velocity of that object and the second derivative tells you the accelleration.
Power Rule:
Sum Rule:
Difference Rule:
Product Rule:
Quotient Rule:
Chain Rule:
Intergals
Like multiplication and division, and addition and subtraction, differentiation has it's opposite. This opposite is called integration. Integration will tell you the area under a curve. Integration is responsible for giving us much of geometry. Lets say we had a barrel shape and wanted to it's area. Well we know that if we take a rectangular slice of the barrel we can find it's area by multiplying it's length and height.
If we take smaller and smaller slices of the barrel and add them together we will get more accurate approximation to the barrels area (as shown above). If we take the limit as our slice size (x vaule) goes to infinity then we end up with EXACTLY the area of the barrel.
Doing this is an arduous process (one which no doubt your Calc teacher will delight inflicting upon you so you will understand what is happening by taking the intergal). Luckily there are a few tricks to taking intergals that make it much easier. Taking an intergal is unfortunatly not as straight foreward and concrete in "how to do it" as other things in math. There are many ways to take intergals and if you choose the wrong path you will probly get the wrong answer. Below is an outline of some of the tricks to taking intergals.
