For our eLearning project in our university, we are using Java applets to show some interactive stuff (like some interactive function plotting or some simple question/answer
Java applets were modern at the beginning of this century. There are only a few sites using Java applets today and this may be one of the reasons why the browser support is not optimal.
From what I've seen before my browser got stuck, your applets seem to be just drawing various charts.
I would suggest trying one of the modern JavaScript libraries which focus on drawing charts: http://javascript.open-libraries.com/utilities/chart/20-best-javascript-charting-and-plotting-libraries/
Alternatively, if you need more options than the libraries offer and you do not care much about cross-browser compatibility, you may use the <canvas> HTML5 element and SVG - all browsers except for Internet Explorer have decent support of these.
If you do not require the charts being interactive, you can render them on the server using PHP, Ruby, Python, Java, or whatever and send them as plain images to the browser.
If you need to express mathematical expressions, consider MathML or plain images possibly rendered on the fly by a server script.