Key Concepts from Calculus I, Prereqs

These notes cover approximately what you'll need to review going into Calculus, if you're in a course that uses this textbook. Some of this may be covered in Chapter 1.

Precalculus

Difference of squares

Sum of cubes

Difference of cubes

change of base formulas

Factorial

Factorial Can be defined as multiplying the first n natural numbers, or recursively as follows:

Sigma Notation(Summation)

Adding up the first 10 natural numbers

can be rewritten as

the index variable, here, can be part of an expression, or it can be used as just an index, as with the following

In this example, has no real meaning, other than to help stand for etc.

Sigma notation properties

Sums and powers of integers

n choose r (AKA nCr or binomial coefficients)

Binomial theorem

Trig Identities

Side ratios (SohCahToa and ChoShaCao)

Pythagorean Identities

Angle Sum formulas

Double Angle formulas

Power reduction formulas