Extending the Algebraic Manipulability of Differentials

Abstract

Treating differentials as independent algebraic units have a long history of use and abuse. It is generally considered problematic to treat the derivative as a fraction of differentials rather than as a holistic unit acting as a limit, though for practical reasons it is often done for the first derivative. However, using a revised notation for the second and higher derivatives will allow for the ability to treat differentials as independent units for a much larger number of cases.

8 pages

Cited by in corpus (3)

• General Representation of Nonlinear Green's Function for Second Order Differential Equations Nonlinear in the First Derivative
• Total and Partial Differentials as Algebraically Manipulable Entities
• Simplifying and Refactoring Introductory Calculus