Dynamic visualization of line integrals of vector fields: a didactic proposal

ABSTRACT

In this paper we present two simulations designed with GeoGebra that illustrate dynamically a key concept in Vector Calculus: line integrals of vector fields, along with other associated mathematical properties and applications. Students are not required to know the GeoGebra environment: a user-friendly interface with buttons, functionalities and online help and exemplar problems allows immediate use of the simulations. The goal of the simulations is to enhance student insight, in the spirit of learning by experimentation, by analysing the dynamic representations provided by the simulations and by dragging objects and changing the parameters involved. The numerical results can be confirmed for special cases by standard undergraduate calculations.

KEYWORDS:

• Calculus
• line integral
• flux
• work
• vector field
• simulation
• interactive
• GeoGebra

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

J. C. Ponce Campuzano  http://orcid.org/0000-0003-4402-1332

Notes

1 Available on the Science and Mathematics Simulations website [11, see] and the GeoGebra website [12, 13, see].

2 A connected curve that does not cross itself and ends at the same point where it begins.