Calculus prerequisites?

Question

I'm not talking about the classes I need to take, but in general the concepts that are heavily used in Calculus. Like the things you need to know cold.

Answer 1

Almost everything you learn before taking calculus is needed in calculus.

You need to have a thorough understanding of "functions". Without having an understanding of functions you can't do calculus. To study functions, you need a good understanding of various other things: The types of functions: here is a good way to remember them:

ILATE:

I: Inverse trigonometric functions

L: Logarithmic functions

A: Algebraic functions

T: Trigonometric functions

E: Exponential functions

for "Trigonometric functions" your trigonometric identities should be at your finger tips

for "Inverse trigonometric functions" you need knowledge of "Trigonometric functions".

for "Algebraic functions" as you can guess, your algebra must be strong (it also includes curve sketching)

"Exponential functions" and "Logarithmic functions" are complementary to each other. For exponential functions you need to have an idea of the constant "e". The knowledge of "e" comes from the "binomial theorem" and the "binomial theorem" can be understood by understanding "permutations and combinations"

So you see, you need EVERYTHING to understand calculus

Answer 2

Look over this paper and see if you know everything on it.

Answer 3

You need a really good grasp on the basics.  Understand logs, powers, fractions and whatnot.  I don't necessarily mean how to do them as much as the concepts behind them.  It helps greatly.

Answer 4

Solving quadratic equations comes up fairly often, but the main things you would want to remember are:

How to factor, reduce, combine algebraic fractions, and otherwise simplify and manipulate equations.

Rules of exponents and logarithms

Trigonometric properties (the functions, basic identities, the unit circle)

Equations for lines (slope, intercept)

Other than that... graphing, function notation, and other basic things like that. If you did alright with the above, it shouldn't be too much of a transition.

Calculus introduces a new way of looking at problems, some new operators, and some applications. Basically, calculus teaches to look at how things act as you get closer to doing something that you cannot do directly; then it teaches methods and shortcuts of doing them.

If you can understand the ideas and remember the methods (which aren't too bad if they are explained well so that they make sense), then the only hard part would be not forgetting algebraic rules or not seeing what method to use on a problem.

Answer 5

Generally a first year calculus class will cover the following:

Limits and their proofs

Differentiation

Integration

Things you'll need to have memorized beforehand:

Factoring

Quadratic formulas

Fractions (being able to change bases, split apart, combine, etc...)