Do It by Yourself: An Instructional Derivation of the Laplacian Operator in Spherical Polar Coordinates

For scientists and engineers, the Laplacian operator is a fundamental tool that has made it possible to carry out important frontier studies involving wave propagation, potential theory, heat conduction, the distribution of stresses in a deformable solid and quantum mechanics. Knowing, understanding...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Ana Laura Pérez-Martínez, Maria del Pilar Aguilar-Del-Valle, Arturo Rodríguez-Gomez
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Laplacian operator spherical polar coordinates undergraduate mathematics Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/d1a5c81885534a2e9462736790204907
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:d1a5c81885534a2e9462736790204907
record_format	dspace
spelling	oai:doaj.org-article:d1a5c81885534a2e94627367902049072021-11-25T18:17:23ZDo It by Yourself: An Instructional Derivation of the Laplacian Operator in Spherical Polar Coordinates10.3390/math92229432227-7390https://doaj.org/article/d1a5c81885534a2e94627367902049072021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2943https://doaj.org/toc/2227-7390For scientists and engineers, the Laplacian operator is a fundamental tool that has made it possible to carry out important frontier studies involving wave propagation, potential theory, heat conduction, the distribution of stresses in a deformable solid and quantum mechanics. Knowing, understanding, and manipulating the Laplacian operator allows us to tackle complex and exciting physics, chemistry, and engineering problems. In this paper, contained in the Special Issue “Mathematics as the M in STEM Education”, we present an instructional derivation of the Laplacian operator in spherical coordinates. Our derivation is self-contained and employs well-known mathematical concepts used in all science, technology, engineering, and mathematics (STEM) disciplines. Our lengthy but straightforward procedure shows that this fundamental tool in mathematics is not intractable but accessible to anyone who studies any of the STEM disciplines. We consider that this work may be helpful for students and teachers who wish to discuss the derivation of this vital tool from an elementary approach in their courses.Ana Laura Pérez-MartínezMaria del Pilar Aguilar-Del-ValleArturo Rodríguez-GomezMDPI AGarticleLaplacian operatorspherical polar coordinatesundergraduate mathematicsMathematicsQA1-939ENMathematics, Vol 9, Iss 2943, p 2943 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Laplacian operator spherical polar coordinates undergraduate mathematics Mathematics QA1-939
spellingShingle	Laplacian operator spherical polar coordinates undergraduate mathematics Mathematics QA1-939 Ana Laura Pérez-Martínez Maria del Pilar Aguilar-Del-Valle Arturo Rodríguez-Gomez Do It by Yourself: An Instructional Derivation of the Laplacian Operator in Spherical Polar Coordinates
description	For scientists and engineers, the Laplacian operator is a fundamental tool that has made it possible to carry out important frontier studies involving wave propagation, potential theory, heat conduction, the distribution of stresses in a deformable solid and quantum mechanics. Knowing, understanding, and manipulating the Laplacian operator allows us to tackle complex and exciting physics, chemistry, and engineering problems. In this paper, contained in the Special Issue “Mathematics as the M in STEM Education”, we present an instructional derivation of the Laplacian operator in spherical coordinates. Our derivation is self-contained and employs well-known mathematical concepts used in all science, technology, engineering, and mathematics (STEM) disciplines. Our lengthy but straightforward procedure shows that this fundamental tool in mathematics is not intractable but accessible to anyone who studies any of the STEM disciplines. We consider that this work may be helpful for students and teachers who wish to discuss the derivation of this vital tool from an elementary approach in their courses.
format	article
author	Ana Laura Pérez-Martínez Maria del Pilar Aguilar-Del-Valle Arturo Rodríguez-Gomez
author_facet	Ana Laura Pérez-Martínez Maria del Pilar Aguilar-Del-Valle Arturo Rodríguez-Gomez
author_sort	Ana Laura Pérez-Martínez
title	Do It by Yourself: An Instructional Derivation of the Laplacian Operator in Spherical Polar Coordinates
title_short	Do It by Yourself: An Instructional Derivation of the Laplacian Operator in Spherical Polar Coordinates
title_full	Do It by Yourself: An Instructional Derivation of the Laplacian Operator in Spherical Polar Coordinates
title_fullStr	Do It by Yourself: An Instructional Derivation of the Laplacian Operator in Spherical Polar Coordinates
title_full_unstemmed	Do It by Yourself: An Instructional Derivation of the Laplacian Operator in Spherical Polar Coordinates
title_sort	do it by yourself: an instructional derivation of the laplacian operator in spherical polar coordinates
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/d1a5c81885534a2e9462736790204907
work_keys_str_mv	AT analauraperezmartinez doitbyyourselfaninstructionalderivationofthelaplacianoperatorinsphericalpolarcoordinates AT mariadelpilaraguilardelvalle doitbyyourselfaninstructionalderivationofthelaplacianoperatorinsphericalpolarcoordinates AT arturorodriguezgomez doitbyyourselfaninstructionalderivationofthelaplacianoperatorinsphericalpolarcoordinates
_version_	1718411407233384448

Do It by Yourself: An Instructional Derivation of the Laplacian Operator in Spherical Polar Coordinates

Ejemplares similares