Sigma / Summation Notation
Summation is something that is done quite often in mathematics, and there is
a symbol that means summation. That symbol is the capital Greek letter
sigma, and so the notation is sometimes called Sigma Notation instead of
Summati
Defining a Sequence
There are two common ways to define a sequence by specifying the general
term.
General Term, an
The first is to use a form that only depends on the number of the term, n. To
find the first five terms when you know the general term, sim
In the past, we have been working with rectangular equations, that is
equations involving only x and y so that they could be graphed on the
Cartesian (rectangular) coordinate system.
We also had an example of the height of a freely falling body as a funct
Matrix Multiplication
Amn Bnp = Cmp
The number of columns in the first matrix must be equal to the number
of rows in the second matrix. That is, the inner dimensions must be the
same.
The order of the product is the number of rows in the first matrix by
The Inverse of a Matrix
So, what is the inverse of a matrix?
Well, in real numbers, the inverse of any real number a was the number a-1,
such that a times a-1 equaled 1. We knew that for a real number, the inverse of
the number was the reciprocal of the n
The need for proof
Most people today are lazy. We watch way too much television and are
content to accept things as true without question.
If we see something that works a few times in a row, we're convinced that it
works forever.
Regions of a Circle
Cons
Heron's Formula
If you know the lengths of the three sides of the triangle, you can use Heron's
Formula to find the area of the triangle.
In Heron's formula, s is the semi-perimeter (one-half the perimeter of the
triangle).
s = 1/2 ( a + b + c )
Area = sq
A geometric sequence is a sequence in which the ratio consecutive terms is
constant.
Common Ratio
Since this ratio is common to all consecutive pairs of terms, it is called the
common ratio. It is denoted by r. If the ratio between consecutive terms is no
Gaussian Elimination
Write a system of linear equations as an augmented matrix
Perform the elementary row operations to put the matrix into rowechelon form
Convert the matrix back into a system of linear equations
Use back substitution to obtain all th
Converting Systems of Linear Equations to Matrices
Each equation in the system becomes a row. Each variable in the system
becomes a column. The variables are dropped and the coefficients are placed
into a matrix. If the right hand side is included, it's c
Each branch of mathematics has its own fundamental theorem(s). If you
check out fundamental in the dictionary, you will see that it relates to the
foundation or the base or is elementary. Fundamental theorems are important
foundations for the rest of the
Determining Conic Sections by Inspection
To determine the conic section by inspection, complete any squares that are
necessary, so that the variables are on one side and the constant is on the
right hand side. Any squared variable below could be replaced
Classical / Theoretical Probability
If outcomes are equally likely, then the probability of an event occurring is the
number in the event divided by the number in the sample space.
P(E) = n(E) / n(S)
The probability of rolling a six on a single roll of a
Binomials raised to a power
A binomial is a polynomial with two terms. We're going to look at the Binomial
Expansion Theorem, a shortcut method of raising a binomial to a power.
(x+y)0 = 1
(x+y)1 = x + y
(x+y)2 = x2 + 2xy + y2
(x+y)3 = x3 + 3x2y + 3xy2 +
An arithmetic sequence is a sequence in which the difference between
consecutive terms is constant.
Common Difference
Since this difference is common to all consecutive pairs of terms, it is called
the common difference. It is denoted by d. If the differe