Edit in JSFiddle

//Bottom Button clicks to scroll down
$("#sidenav-bottombtn").click(function(){
     $('#sidenav ul').animate({scrollTop: '+=300px'}, 800);
});
//Top Button animates to scroll up
$("#sidenav-topbtn").click(function(){
    $('#sidenav ul').animate({scrollTop: '-=300px'}, 800);
 });

//Finds height between ul and li.selected
var selected = $("#sidenav ul li.selected");
var offset = selected.offset();

//ScrollTop to offset
$('#sidenav ul').animate({scrollTop: $(selected).offset().top/1.65 }, 'fast');

<article role="article" id="sidenav">
<div id="sidenav-topbtn"><img src="http://www.chrisdivyak.com/jsfiddle/topbtn.png" alt="Top Button"></div>

<ul id="nav-sub" class="daymenu">
    <li><a href="#">Overview</a></li>
    <li><a href="#">Theories, Definitions &amp; Concepts</a></li>
    <li><a href="#">Getting Started</a></li>
    <li><a href="#">Three Societal Systems</a></li>
    <li><a href="#">Political System</a></li>
    <li><a href="#">Distribution of Wealth</a></li>
    <li><a href="#">Economic System</a></li>
    <li class="selected"><a href="#">Communications System</a></li>
    <li><a href="#">Hierarchies of Knowledge</a></li>
    <li><a href="#">Interrelated Systems of Power</a></li>
    <li><a href="#">Popping the Bubble</a></li>
    <li><a href="#">Knowledge » Wealth » Power</a></li>
    <li><a href="#">Knowledge is not power, but allows one to gain or exercise power</a></li>
    <li class="last"><a href="#">Conclusion</a></li>
</ul>

<div id="sidenav-bottombtn"><img src="http://www.chrisdivyak.com/jsfiddle/bottombtn.png" alt="Bottom Button"></div>
</article>

img{
	padding:10px;
	position:relative;
	display: block;
    margin-left: auto;
    margin-right: auto;
	}
#sidenav-topbtn,
#sidenav-bottombtn{
	background:#ccc;
	padding:10px;
}
#sidenav-topbtn img,
#sidenav-bottombtn img{
	margin-bottom:0;
	margin-top:0;
	border:none;
}
#sidenav{
	padding:0;
	height: 100%;
	top: 0;
	left: 0;
	height:100%;
	z-index: 99999;
	background:url('../images/bg.jpg');
	background-repeat: repeat;
	display:block;
	background-position: center center;
	*left:0;

	}
#sidenav ul{
	padding:0;
	margin:0;
	max-height:300px;/*shows 5 items*/
	overflow:hidden;
	}
#sidenav li a{
	display:block;
	padding: 20px;
	color:#226099;
	line-height: 1.2em;
    font-size:0.8em;
	-webkit-transition: background 300 ease-in-out;
	-moz-transition: background 300 ease-in-out;
	-ms-transition: background 300 ease-in-out;
	-o-transition: background 300 ease-in-out;
	transition: background 300 ease-in-out;
	}
#sidenav li a:hover{
	color:#226099;
	background: #d3dae2;
	background: rgba(211,218,226, 0.7);
	}
#sidenav ul li{
	border-bottom:1px solid #ccc;
	width:100%;
	list-style:none;
	font-size: 1.8em;
	}
#sidenav li.selected a  {
	background: #fff;
	background:rgba(255,255,255,0.8);
	color: #465364;
	position:relative;
	z-index:0;
	}

#sidenav li.selected a:before {
		content: '\2192';
		margin-right: 3px;
		}