It is in the field of numerical analysis that this "easy-looking" function, also known as the Runge function, exhibits a behavior so idiosyncratic that it is mentioned even in most undergraduate textbooks. In spite of the fact that the function is infinitely differentiable, the common procedure of (uniformly) interpolating it with polynomials that…

A novel approach for teaching interpolation in the introductory course in numerical analysis is presented. The interpolation problem is viewed as a problem in linear algebra, whence the various forms of interpolating polynomial are seen as different choices of a basis to the subspace of polynomials of the corresponding degree. This approach…

How to determine when there is a unique solution when two sides and an angle of a triangle are known, using simple algebra and the law of cosines, is described. (MNS)

Discusses a numerical technique called the method of adjoints, turning a linear two-point boundary value problem into an initial value problem. Described are steps for using the method in linear or nonlinear systems. Applies the technique to solve a simple pendulum problem. Lists 15 references. (YP)

Reviews the underpinnings of synthetic division. Shows how to quickly obtain the coefficients of the Taylor expansion of a polynomial about a point, and a partial fraction decomposition of a polynomial. (MVL)

Presents an approach to Vieta's formula involving pi and infinite product expansions of the sine and cosine functions. Indicates how the formula could be used in computing approximations of pi. (MVL)

In this article, the author proves a theorem about polynomial zeros, but the focus is on how the theorem is integrated into a QuickBASIC computer program, and how that program answers the questions of the theorem--a unification of mathematics and computer programming. For a given polynomial, how can one overcome assorted problems in finding zeros…