How to center a div in the middle of the window?

It is very simple. You just have to make a new function like this:

jQuery.fn.center=function(){
    this.css("position","absolute");
    this.css("top",(($(window).height()-this.outerHeight())/2)+$(window).scrollTop()+"px");
    this.css("left",(($(window).width()-this.outerWidth())/2)+$(window).scrollLeft()+"px");
    return this;
}

Now we can just write:

$(element).center();