Maths - Elements of an equation

An equation is a mathematical expression with an equals sign in it.

Other possible elements of an equation are:

These are explained below:

Numbers

There are different types of numbers, for instance:

and these numbers may be coded in different ways:

Unless otherwise specified we usually assume that numbers are decimal.

Variables

Sometimes an equation contains a number but we don't yet know its value, or we may want to apply the equation to a range of values.

An example of the first is using x as the unknown, for example,

x + 1 = 3

An example of the second might be an equation of a line:

y = 2 * x + 3

In general we use:

x, y, z for unknowns.

a, b, c for values which are not yet specified.

Binary Operators

The operators:

take the two numbers on either side and replace it by a single number.

Addition

In the following plot the height is given by a+b, this gives a flat plane at 45° to both a and b:

add

how this graph was produced

Of course the plane is infinite in all directions but here we have only shown a section of the plane.

Multiplication

In the following plot the height is given by a*b, this gives a surface made up of straight lines along a or b directions (bi-linear). If we take a direction at 45° to both a and b then we get a parabola.

multiply

how this graph was produced

Unary operators

The operators:

apply to the number to the right. '-' inverts the number (subtracts from 0) '+' says the number to the right is positive (the default).

Brackets

When we mix + and * then the answer we get depends on the order that we apply them.

For example

2 + 1 * 3

To clarify this we can put brackets around the operation to be applied first:

(2 + 1) * 3 = 9

2 + (1 * 3) = 5

If we don't specify which has precedence by using bracket then by default * and ÷ have precedence over + and -. So,

2 + 1 * 3 = 5

Functions

A function takes one number and uses it to generate another number. For example the function sin() takes an angle as input and returns the ratio of opposite and hypotenuse in a right angled triangle.


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