OnlineUniversities.com released this blog post on May 30th. They have compiled their recommendations for the 50 Best iPad apps for STEM. I like how the blog post starts off with "General" STEM apps recommendations and then addresses S, T, E, M individually with apps that meet those individual fields.
So, take a look at their list. If you fill they have overlooked some great STEM apps share them as responses to this post and together we can collaboratively build our own list.