Where to Go From Here?
You can download the completed project over here.
I hope you enjoyed your trip into the numerical world, learned a few things about algorithms, and even a few fun facts about the ancient world to help you on your next trivia night.
Before you start exploring more, you should play with different values for deltaT, but keep in mind that playgrounds are not that fast and choosing a small step size can freeze Xcode for a long time -- my MacBook froze for several minutes after I changed deltaT to 0.01 to make the second Euler screenshot.
With the algorithms you learned, you can solve a variety of problems like the n-body problem.
If you are feeling a little shaky about algorithms in general, you should check out MIT's Introductions to Algorithms class on YouTube.
Finally, keep check back to the site for more tutorials on this subject.
If you have questions or ideas about other ways to use numerical algorithms, bring it to the forums by commenting below. I look forward to hearing your thoughts and talking about all the cool things math can do for your apps.
