2007-08-05, by Ayal Pinkus
Fun with derivatives part 4: Newton iteration to determine the inverse square root - A while back I came across the trick used in Quake to efficiently approximate the inverse square root (which is probably needed in a 3D engine to normalize vectors). It is also a nice demonstration on how one could go about approximating a function by using Newton iteration. That is the subject of this article.

2007-08-05, by Ayal Pinkus
Fun with derivatives part 3: fast convergence of Newton iteration - Newton iteration is a natural fit for computer algebra systems because you can use the symbolic facilities first to take the derivative of a function, and then later on use the arbitrary-precision numeric support to get a very accurate numeric approximation (starting from a sufficiently close guess). Newton iteration can converge very fast, which you can see in action in this article.

2007-08-05, by Ayal Pinkus
Fun with derivatives part 2: Taylor series expansions - This short article shows how you one would go about writing one line of code that generates a Taylor series expansion of a function in Yacas (without using the built-in function).

2007-07-20, by Ayal Pinkus
Fun with derivatives part 1: defining the concept of a derivative in Yacas - Taking a derivative is one of the mathematical operations that is easily explained to a computer. This article shows how it can be done with a few lines of code in Yacas. You can also directly try it out, or extend the code to handle more complex cases.