Why won’t the Jquery validation plugin work?

You are mixing PHP and Javascript.

The part between <script> must not be in the PHP code, but you could put it in the variable just after </form>.

Another way of doing it would be to create a Javascript file myfunctions.js, putting the code into it and enqueueing it.

The code would be:

add_action( 'wp_enqueue_script', 'load_jquery2' );
function load_jquery2() {
    wp_enqueue_script( 'jquery' );
}      

function add_my_css_and_my_js_files(){
    wp_enqueue_script('jquery-validate-min', plugins_url('activate/jquery_validate_min.js', __FILE__ ) );
}
add_action('wp_enqueue_scripts', "add_my_css_and_my_js_files");


function mp_calcs_display() {
return '
<form name="calsinput" action="" method="post" id="calsinput" >
<h1> Process </h1>
<p> operation type always robot </p>
<br> <br>
Number of welds: <input type="number" name="numberofwelds" class="required digits" title="This field is required and must be a no."  >
<br> <br>
Number of construction welds: <input type="number" name="numberofconwelds" class="required digits"  title="This field is required and must be a no.">
<input type="submit" value="Calculate cycle time ">
</form>
<script type="text/javascript">
    jQuery(document).ready(function($) {
        $("#calsinput").validate();
    });  
</script>';
}