The definition of a Taylor polynomial of order k of a function f at a point xo implies that the degree of this polynomial is at most k, but it can be smaller than k (if f (k)(x0) = 0). It is plain to ...

We solve polynomials algebraically in order to determine the roots - where a curve cuts the \(x\)-axis. A root of a polynomial function, \(f(x)\), is a value for \(x\) for which \(f(x) = 0\).

Problem 1: Approximate (sin(x)) using a truncated Taylor series expansion. The function takes inputs (x) and truncation order (N), returning the series approximation. Truncation errors are analyzed by ...

In a factorial ring, we can define the p.g.c.d. of two elements (defined to the nearest unit) and the notion of prime elements between them. More generally, Bezout’s identity characterizes two prime ...

Abstract: The solution of overdetermined systems of polynomial equations shows promise for solving complicated problems in signal processing and related fields. Polynomials can represent more ...

In a boon to algebra students everywhere, a professor at Carnegie Mellon University has devised a simpler and more efficient way to solve problems involving the quadratic equation. The new method was ...

A function machine is a way of writing rules using a flow diagram. The equation \(3j - 6 = 9\) can be shown on a function machine by writing out the functions that have been applied to \(j\) in the ...