The Hidden Opportunities in the Derivative
Peter F. Erickson
This lecture is taken from the author's book, Absolute Space, Absolute Time, & Absolute Motion. The idea of the limit when applied to the derivative in the infinitesimal calculus is wrong. It does not solve the problem that the derivative is usually different from dy/dx.. Instead, it conceals this problem. As a result of applying the limit idea, certain products of the process of derivation are commonly rejected, leaving only the derivative. Yet, inspection shows that they must still exist. Since the derivative is not an approximation, but an exact product, the commonly rejected extra terms must be recognized as present. As such, they may provide an avenue for the future advance of physical science.
