Change the BootZard validation code

I'm using the step wizard of this site , but I hit a small obstacle. In the code it validates all fields through this excerpt:

parent_fieldset.find('input[type="text"], input[type="password"], textarea').each(function() {
        if( $(this).val() == "" ) {
                $(this).addClass('input-error');
                next_step = false;
        }
        else {
                $(this).removeClass('input-error');
        }
});

But not all fields are required. How do I adapt this section:

$.post("validar.php", $("#contact-form").serialize(), function(response) {                      
       $('#success').html(response);                 
});

In the previous section? If you can not, how would I validate only the fields that need to be validated?

The complete script code is:

function scroll_to_class(element_class, removed_height) {
    var scroll_to = $(element_class).offset().top - removed_height;
    if($(window).scrollTop() != scroll_to) {
        $('html, body').stop().animate({scrollTop: scroll_to}, 0);
    }
}

function bar_progress(progress_line_object, direction) {
    var number_of_steps = progress_line_object.data('number-of-steps');
    var now_value = progress_line_object.data('now-value');
    var new_value = 0;
    if(direction == 'right') {
        new_value = now_value + ( 100 / number_of_steps );
    }
    else if(direction == 'left') {
        new_value = now_value - ( 100 / number_of_steps );
    }
    progress_line_object.attr('style', 'width: ' + new_value + '%;').data('now-value', new_value);
}

jQuery(document).ready(function() {

    /*
        Fullscreen background
    */
    $.backstretch("assets/img/backgrounds/1.jpg");

    $('#top-navbar-1').on('shown.bs.collapse', function(){
        $.backstretch("resize");
    });
    $('#top-navbar-1').on('hidden.bs.collapse', function(){
        $.backstretch("resize");
    });

    /*
        Form
    */
    $('.f1 fieldset:first').fadeIn('slow');

    $('.f1 input[type="text"], .f1 input[type="password"], .f1 textarea').on('focus', function() {
        $(this).removeClass('input-error');
    });

    // next step
    $('.f1 .btn-primary').on('click', function() {
        var parent_fieldset = $(this).parents('fieldset');
        var next_step = true;
        // navigation steps / progress steps
        var current_active_step = $(this).parents('.f1').find('.f1-step.active');
        var progress_line = $(this).parents('.f1').find('.f1-progress-line');

        // fields validation

            parent_fieldset.find('input[type="text"], input[type="password"], textarea').each(function() {
                    if( $(this).val() == "" ) {
                            $(this).addClass('input-error');
                            next_step = false;
                    }
                    else {
                            $(this).removeClass('input-error');
                    }
            });

        // fields validation

        if( next_step ) {
            parent_fieldset.fadeOut(400, function() {
                // change icons
                current_active_step.removeClass('active').addClass('activated').next().addClass('active');
                // progress bar
                bar_progress(progress_line, 'right');
                // show next step
                $(this).next().fadeIn();
                // scroll window to beginning of the form
                scroll_to_class( $('.f1'), 20 );
            });
        }

    });

    // previous step
    $('.f1 .btn-previous').on('click', function() {
        // navigation steps / progress steps
        var current_active_step = $(this).parents('.f1').find('.f1-step.active');
        var progress_line = $(this).parents('.f1').find('.f1-progress-line');

        $(this).parents('fieldset').fadeOut(400, function() {
            // change icons
            current_active_step.removeClass('active').prev().removeClass('activated').addClass('active');
            // progress bar
            bar_progress(progress_line, 'left');
            // show previous step
            $(this).prev().fadeIn();
            // scroll window to beginning of the form
            scroll_to_class( $('.f1'), 20 );
        });
    });

    // submit
    $('.f1').on('submit', function(e) {

        // fields validation

        $(this).find('input[type="text"], input[type="password"], textarea').each(function() {
            if( $(this).val() == "" ) {
                e.preventDefault();
                $(this).addClass('input-error');
            }
            else {
                $(this).removeClass('input-error');
            }
        });

        // fields validation

    });

});

And the HTML:

<div class="form-group">
   <label class="sr-only" for="f1-last-name">Last name</label>
   <input type="text" name="f1-last-name" placeholder="Last name..." class="f1-last-name form-control" id="f1-last-name">
</div>
<div class="form-group">
    <label class="sr-only" for="f1-about-yourself">About yourself</label>
    <textarea name="f1-about-yourself" placeholder="About yourself..." class="f1-about-yourself form-control" id="f1-about-yourself"></textarea>
</div>
<div class="f1-buttons">
    <button type="button" class="btn btn-primary">Próximo</button>
</div>