datepicker and validation

HTML

<link rel="stylesheet" href="http://code.jquery.com/ui/1.10.3/themes/smoothness/jquery-ui.css">
<script src="http://code.jquery.com/ui/1.10.3/jquery-ui.js"></script>
<script src="http://ajax.aspnetcdn.com/ajax/jquery.validate/1.10.0/jquery.validate.js"></script>
<form action="#">
    <input id="StartDate" name="StartDate"  type="date" />
    <input id="EndDate" name="EndDate"  type="date" />
    <input type="submit" />
</form>
<br />
<div style="height: 800px">
    gotat
</div>

JavaScript

$(document).ready(function () {
            
            validate_start_date('StartDate');
            validate_end_date('StartDate', 'EndDate');
             });

function validate_start_date(start) {

    $(`"#${start}"`).change(function () {
        var startDate = document.getElementById(`"${start}"`).value;
        var today = new Date();
        today.setHours(0, 0, 0, 0);

        if (Date.parse(startDate) <= today) {
            alert('The start date cannot be before today.');
            document.getElementById(`"${start}"`).value = '';
        }
    });    
}

function validate_end_date(start, end) {

    $(`"#${end}"`).change(function () {
        var startDate = document.getElementById(`"${start}"`).value;
        var endDate = document.getElementById(`"${end}"`).value;

        if (Date.parse(endDate) <= Date.parse(startDate)) {
            alert('The end date should be greater than the start date.');
            document.getElementById(`"${end}"`).value = '';
        }
    });
}