How many people per day?

I realize this may require some sophisticated data manipulation but there must be a way, I just don’t know how and would appreciate any guidance from the forum. I’m an administrator for a professional development program. I run multiple online courses simultaneously with new participants starting and stopping on a rolling basis. New participants start on one day and may finish in a week, a month or in some cases multiple months later. I have a spreadsheet that tracks, among other things, the course a participant took, the date they started and the date they finished, so my data set looks something like this:

Course Start Date Finish Date
Course 1 7/7/2014 8/15/2014
Course 1 7/7/2014 8/15/2014
Course 2 7/7/2014 8/6/2014
Course 3 7/7/2014 8/1/2014
Course 3 7/11/2014 8/15/2014
Course 2 7/17/2014 8/29/2014
Course 2 7/17/2014 8/1/2014
Course 1 7/25/2014 10/10/2014
Course 3 7/25/2014 10/1/2014

My actual data set has almost 2,000 records with a year’s worth of date ranges. I’ve been asked to do an audit that will require me knowing the average daily participation in each course (i.e. how many students are enrolled in each course on any given date). I know how to calculate total days enrolled, that’s pretty easy, but can I do a date reference? For example, can I use this data set to calculate/reference how many students were enrolled in Couse 2 on date X? I’ve thought about trying to do this with a pivot table? A Gnatt chart? Calculating days lapsed and plotting on a chart of some sort, but nothing has worked so far.