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CS101 - Introduction to Computing - Lecture Handout 35

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Mathematical Methods

(Web Development Lecture 12)

During the last lecture we discussed Event handling:

We looked at the concept of event-driven programs and event handlers
What are they?
What do they do?
How do we benefit from them?
We wrote simple programs to demonstrate the capabilities of a few event handlers
What is Event Handling?
Capturing events and responding to them
The system sends events to the program and the program responds to them as they arrive
Events can include things a user does - like clicking the mouse - or things that the system itself does - like updating the clock. Today we will exclusively focus on user-events.

Event Driven Programs:

Programs that can capture and respond to events are called ‘event-driven programs’ JavaScript was specifically designed for writing such programs

JavaScript’s Handling of Events:

Events handlers are placed in the BODY part of a Web page as attributes in HTML tags
Events can be captured and responded to directly with JavaScript one-liners embedded in HTML tags in the BODY portion
Alternatively, events can be captured in the HTML code, and then directed to a JavaScript function for an appropriate response

In-Line JavaScript Event Handling:

Event handlers are placed in the BODY portion of a Web page as attributes of HTML tags
The event handler attribute consists of 3 parts:
The identifier of the event handler
The equal sign
A string consisting of JavaScript statements enclosed in double or single quotes
Multiple JavaScript statements (separated by semicolons) can be placed in that string, but all have to fit in a single line; no newline characters are allowed in that string Due to this limitation, sophisticated event handling is not possible with in-line event handling

Usage Guideline:

For very short scripts, “all code in the tag” works well
The “code in the HEAD portion” is the right choice for developing larger JavaScript scripts
It makes the code easier to read
It allows the reuse of a function for multiple event handlers

onFocus & onBlur:

onFocus executes the specified JavaScript code when a window receives focus or when a form element receives input focus
onBlur executes the specified JavaScript code when a window loses focus or a form element loses focus

onLoad & onUnload:

onLoad executes the specified JavaScript code when a new document is loaded into a window
onUnload executes the specified JavaScript code when a user exits a document.
Mixed-case capitalization of event handlers (e.g. onClick) is a convention (but not a requirement) for JavaScript event handlers defined in HTML code
At times, you may wish to use event handlers in JavaScript code enclosed in <SCRIPT>, </SCRIPT> tags

A Note on Syntax:

In those cases you have to strictly follow the JavaScript rule for all event handler identifiers: they must all be typed in small case, e.g. ‘onclick’ or ‘onmouseover’

Today’s Goal:(Mathematical Methods)

We will look at JavaScript’s Math object
We will look at solutions for simple problems using various methods of the Math object

Problems & Solutions:

JavaScript doesn’t support drawing of graphics
However, crude graphics can be put together with the help of various text characters or tables
One cannot write a character at a random location on the screen using JavaScript
Instead, the graph has to be drawn from top to bottom, one row at a time – just like when regular text is written to a document

Problems & Solutions

<TITLE>Sine Function Plot</TITLE>
function plotSine( ) {


<BODY onLoad="plotSine( )">
function plotSine( ) {
var ht, wd, rowN ; // rowN is the row number
ht = 15 ; // height of the half cycle
wd = 90 ; // width of the plot
"<H1 align = 'center'>sin(x)</H1>" ) ;
for( rowN = ht; rowN >= -ht; rowN = rowN - 1 ) {
plotRow( rowN, ht, wd ) ;
function writeRow( row, wd ) {
var rowE ;
"<FONT face = 'courier' size = '-2'>" ) ;
for( rowE = 0; rowE <= wd; rowE = rowE + 1 ) {

document.write ( row[ rowE ] ) ;
document.write( "<BR></FONT>" ) ;
function plotRow( rowN, ht, wd ) {
var theta, rowE ; // rowE is the row element
var row = new Array( wd ) ;
for ( rowE=0; rowE <= wd; rowE = rowE + 1 ) {
theta = 2 * Math.PI * rowE / wd ;
if( rowN == Math.round(ht * Math.sin( theta )))
row[ rowE ] = "*" ;
row[ rowE ] = "&nbsp;" ;
writeRow ( row, wd ) ;
function plotRow( rowN, ht, wd ) {
var theta, rowE ;
var row = new Array( wd ) ;
for ( rowE=0; rowE <= wd; rowE = rowE + 1 ) {
theta = 2 * Math.PI * rowE / wd ;
if( rowN == Math.round(ht * Math.sin( theta )))
row[ rowE ] = "*" ;
elseProblems & Solutions 1

row[ rowE ] = "&nbsp;" ;
writeRow ( row, wd ) ;

Problems & Solutions 2

That is a sine wave.
How about a cosine?
Or a tangent?
Or, even, the natural logarithm?

Today We Have Seen 3 New Elements:

A property that gave us the value of Pi
Math.round( )
A method that rounded a number to its nearest integer
Math.sin( )

A method that gave us the sine of an angle
All 3 belong to JavaScript’s Math object

Mathematical Functions in JavaScript:

In addition to the simple arithmetic operations (e.g. +, *, etc.) JavaScript supports several advanced mathematical operations as well
Notationaly, these functions are accessed by referring to various methods of the Math object
Moreover, this object also contains several useful mathematical constants as its properties
This object has no use, but of a placeholder



Properties 1

Returns a randomly-selected, floating-point number between 0 and 1


document.write( Math.random( ) )


random( ):
Design a Web page that displays the result of the rolling of a 6-sided die on user command


<TITLE>Electronic Die</TITLE>
function rollDie( ) { … }
<FORM … > … </FORM>

<FORM name="form1" method="post" action="">
<INPUT type="submit" name="Submit"
value="Roll Die" onMouseOver="rollDie( )">
<INPUT type="text" name="die" size="12">

function rollDie( ) {
var dieN, dieDots, dots ;
dieDots = "* " ;
dieN = Math.round( 6 * Math.random( ) ) ;
for( dots = 2; dots <= dieN; dots = dots + 1 ) {
dieDots = dieDots + "* " ;
document.form1.die.value = dieDots ;

During Today’s Lecture …:

We looked at the properties and methods of JavaScript’s Math object
We produced solutions for simple problems using several methods of the Math object

Next (the 13th) Web Dev Lecture:

String Manipulation
To become familiar with a few methods used for manipulating strings
To become able to solve simple problems involving strings