The Algebraic Structure of Quantity Calculus II: Dimensional Analysis and Differential and Integral Calculus

Abstract

In a previous paper, the author has introduced and studied a new algebraic structure which accurately describes the algebra underlying quantity calculus. The present paper is a continuation of that one, which extends the purely algebraic study by adding two more ingredients: an order structure and a topology. The goal is to give a solid justification of dimensional analysis and differential and integral calculus with quantities.

Keywords

• quantity calculus
• algebraic structure
• dimensional analysis
• pi-theorem