IsisCB Explore

Article ID: CBB766129464

Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics (2015)

Kjeldsen, Tinne Hoff (Author)
Lützen, Jesper (Author)

Science and Education
Volume: 24
Issue: 5
Pages: 543-559

DOI: 10.1007/s11191-015-9746-x

URI: https://doi.org/10.1007/s11191-015-9746-x

Outside Links

WorldCat

Google Scholar

JSTOR

Academia.edu

Mathematics and its relationship to science Mathematics education Physics Mathematics Functions (mathematics) Fourier, Jean Baptiste Joseph Dirichlet, Johann Peter Gustav Lejeune Euler, Leonhard

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit–reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science.

...More

Included in

Article Ricardo Karam (2015) Introduction of the Thematic Issue on the Interplay of Physics and Mathematics. Science and Education (pp. 487-494). unapi

Citation URI

https://data.isiscb.org/isis/citation/CBB766129464/

Citations Indexes

Similar Citations

Book Romano Gatto; (2010)
Libri di matematica a Napoli nel Settecento. Editoria, fortuna e diffusione delle opere (/isis/citation/CBB036073323/)

Article Loredana Biacino; (2018)
The Concept of Function at the Beginning of the 20th Century: A Historiographical Approach (/isis/citation/CBB435431910/)

Article González Redondo, Francisco A.; (2002)
Daviet de Foncenex y Lazare Carnot: ¿Las raíces dimensionales de Fourier? Algunos comentarios a Martins, Grattan-Guinnes y Gillespie (/isis/citation/CBB000300774/)

Article Guo, Jinhai; (2014)
William Fogg Osgood and the Dissemination of Theories of Functions in China (/isis/citation/CBB001214103/)

Book Paul J. Nahin; (2020)
Hot Molecules, Cold Electrons: From the Mathematics of Heat to the Development of the Trans-Atlantic Telegraph Cable (/isis/citation/CBB042236017/)

Article Ferraro, Giovanni; (2007)
Convergence and Formal Manipulation in the Theory of Series from 1730 to 1815 (/isis/citation/CBB000771368/)

Article Coates, John; (2008)
Euler's Work on Zeta and L-Functions and Their Special Values (/isis/citation/CBB000931916/)

Article Ferraro, Giovanni; (2004)
Differentials and Differential Coefficients in the Eulerian Foundations of the Calculus (/isis/citation/CBB000410838/)

Article Ferraro, G.; (2000)
Functions, Functional Relations, and the Laws of Continuity in Euler (/isis/citation/CBB000110926/)

Article Heeffer, Albrecht; (2012)
The Genesis of the Algebra Textbook: From Pacioli to Euler (/isis/citation/CBB001320800/)

Thesis Fiss, Andrew; (2011)
Professing Mathematics: Science and Education in Nineteenth-Century America (/isis/citation/CBB001562818/)

Book van Brummelen, Glen; (2013)
Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry (/isis/citation/CBB001214093/)

Article Atkinson, Leigh; (2002)
Where do Functions Come From? (/isis/citation/CBB000202520/)

Article Tazzioli, Rossana; (2001)
Green's Function in Some Contributions of 19th Century Mathematicians (/isis/citation/CBB000100594/)

Article Bueno, Otávio; (2005)
Dirac and the Dispensability of Mathematics (/isis/citation/CBB000771648/)

Article Hayashi, Haruo; (1999)
The Influence of Fourier on W. Thomson (/isis/citation/CBB000330326/)

Article Darrigol, Olivier; (2007)
The Acoustic Origins of Harmonic Analysis (/isis/citation/CBB000772559/)

Book Ronald S. Calinger; (2015)
Leonhard Euler: Mathematical Genius in the Enlightenment (/isis/citation/CBB749253216/)

Book Henry, Philippe; (2007)
Leonhard Euler “incomparable géomètre” (/isis/citation/CBB000953060/)

Book Schuster, John; (2013)
Descartes-Agonistes: Physico-Mathematics, Method and Corpuscular-Mechanism 1618--33 (/isis/citation/CBB001500367/)

Comments

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}