类型错误ajax不是函数

I am using JQuery Ajax function with php to check if email exists. This is working fine when using core-php. But when I am integrating the same in Joomla Page using Sourcer, I am getting the error in firebug console.

TypeError: $.ajax is not a function

The total code for JQuery and the form is like this:

<html>
<head>
<script src="form/js/jquery.js"></script>
<script type="text/javascript">
if (window.jQuery) {  
    alert("Jquery loaded!");
} else {
    alert("Jquery not loaded!");
}

function checkemail()
{
 var email=document.getElementById( "Email" ).value;

 if(email)
 {
  $.ajax({
  type: 'post',
  url: 'form/checkdata.php',
  data: {
   user_email:email,
  },
  success: function (response) {
   $( '#email_status' ).html(response);
   if(response=="OK")   
   {
    return true;    
   }
   else
   {
    return false;   
   }
  }
  });
 }
 else
 {
  $( '#email_status' ).html("");
  return false;
 }
}

function checkall()
{

 var emailhtml=document.getElementById("email_status").innerHTML;

 if((emailhtml)=="OK")
 {
  return true;
 }
 else
 {
  return false;
 }
}

</script>
</head>
<body>

<form method="POST" action="insertdata.php" onsubmit="return checkall();">

 <input type="text" name="email" id="Email" onkeyup="checkemail();">
 <span id="email_status"></span>
 <br>
 <input type="password" name="userpass" id="UserPassword">
 <br>
 <input type="submit" name="submit_form" value="Submit">
</form>

</body>
</html>