OK...this is a really trivial question, but I hope someone can help me here. I am working on building a segway-style robot that balances on two wheels, but I am having some difficulties integrating the data I receive from my gyro sensor. The sensor gives me the angular velocity, and I know that to find the actual tilt angle I need to use something like RK4. However, I have not taken differential equations, just Calculus AB, and I am having trouble understanding exactly what Runge-Kutta integration does. I looked all over the place, from Mathworld to Wikipedia, and I feel that I am close to getting it, but the f(x,y) keeps throwing me off. Could someone please explain in more basic terms what I need to be doing? [Edit] I realize that I need to be a bit more specific. If my first 5 seconds of data are represented as ordered pairs (time t, angular velocity at time t) and I know that the angle is 0 at time t, how would I integrate (0,0), (1, 3), (2, 5), (3, 3), (4, 2), (5, 6) using, say, RK4? If you need more information, let me know.