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

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...

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Bibliographic Details
Published in:Measurement science review 2019-04, Vol.19 (2), p.70-78
Main Author: Raposo, Álvaro P.
Format: Article
Language:English
Subjects:
Algebra
algebraic structure
Calculus
Differential calculus
Dimensional analysis
Integral calculus
Mathematical analysis
pi-theorem
Quantity calculus
Topology
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Summary: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.
ISSN:1335-8871
1335-8871
DOI:10.2478/msr-2019-0012