You were trying to implode an array called field_array, even though your example shows an array called field_arrayfields_array:
$fields_array = array('course','batch','branch');
$fields = implode(", ",$fields_array);
$resource = mysql_query("SELECT $fields FROM some_table") or die(mysql_error());
Edit: You changed your code again. Could you please give us the exact code that you're working with?