You have the following ways:
1 - The simplest - instead of div - use an IFrame similar to this
<div id="search">
<form id="try" method="post" target="receiver" action="url-to-server-Page">
Batch: <input id="batch" name="batch" type="text"/>
Dept: <input id="dept" name="dept" type="text" />
<input type="submit"/>
</form>
</div>
<iframe name="receiver" id="receiver"></iframe>
</div>
, , url-to-server-page, - HTML-, .
, JavaScript .
2 - JavaScript AJAX. , . jQuery - , ... http://jquery.com/
3 -
<div id="search">
<form id="try" method="post" target="receiver" action="url-to-server-Page">
Batch: <input id="batch" name="batch" type="text"/>
Dept: <input id="dept" name="dept" type="text" />
<input type="submit"/>
</form>
<div id="receiver">
<?php if (isset($_POST['batch']) && isset($_POST['dept'])){
}
?>
</div>
</div>