**Iteration and Higher mathematics**

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**Iteration **

**Mathematics.** A computational procedure in which a cycle of
operations is repeated, often to approximate the desired result more
closely.

**Computer Science.**

- The process of repeating a set of instructions mamy times or until a specific result is achieved.
- A cycle of a set of instructions to be repeated:
*After ten
iterations, the program exited the loop.*

**Mathematics Application:**

**Algebra - **In algebra you learned to solve equations for **X. **Your
teacher may have told you to check your answer by substituting that number into
the equation. If your answer resulted in a equality, you can be certain
that your answer was correct. With a computer you can skip solving the
equation and simply search for the solution by testing every number in a finite
set of numbers. For example, if you knew that X was an Integer between
-1000 and +1000 you would have to do 2000 iteration to find all the
solution. Programmers use looping to perform repetitive operations.

**Calculus - **We use calculus to calculate the area under a curve of
continuous function of **x**. We can approximate the area under a curve
with a number of rectangles with height **f(x)** and width of delta x).
The smaller the value of delta x the greater the number rectangles required
cover the bounded area. One iteration or loop is required to calculate
area of each rectangle.

**JavaScript Methods of Looping - **Before doing any physics or
electronics calculations let us consider some methods of looping.

**Warning: **Infinite
Loops can hang up your computer.** Pressing Ctrl/Alt/Delete **buttons
simultaneously will interrupt program operation and cause **Windows Task
Manager** Menu to be displayed. Use **Windows Task Manager
- ** **End Task **button to stop your program.

**For **Keyword**: **

The for loop uses an index counter to keep track of the number loops, and
stops looping when a certain number is reached.

<HTML>

<head>

<TITLE>Simple Script 1</TITLE>

</head>

<Body>

<SCRIPT LANGUAGE = JavaScript>

n = 10

for (i = 1; i < 8; i++){

n = n *n;

alert("n = "+n)

}

alert("The End")

</SCRIPT>

</Body>

</HTML>

**Notes:**

i = 1 is start count.

i < 8 defines upper limit

i++ means i = i + 1 or simply increment i.

**Statements in parenthesis ( ) control loop.**

Statements in wiggly parenthesis {} are operations to be performed in each
loop.