Bibliographic Details
| Title: |
Resolviendo dv/dt = 𝜹(t), v(0) = 0: Una propuesta pedagógica desde la física y la matemática avanzada. |
| Authors: |
Gutiérrez, Ranferí1 mrgutierrez@uvg.edu.gt, Sigüenza, María2 |
| Source: |
Latin-American Journal of Physics Education. Sep2025, Vol. 19 Issue 3, p1-6. 6p. |
| Subject Terms: |
*Teaching methods, *Intuition, Dirac function, Impulse (Physics), Differential equations, Classical mechanics, Laplace transformation, Initial value problems |
| Abstract (English): |
This article presents a didactic strategy to support students in understanding the initial value problem 𝜹(t), v(0) = 0:, and its solution v(t) = 1, where the Dirac delta function appears as part of the differential equation. The approach consists of interpreting the problem in terms of a physical situation involving a particle initially at rest, subjected to an impulsive force. By first analyzing an elementary problem in classical mechanics--where a known force acts over a finite time interval--students can comprehend the role of impulse and how it translates into changes in velocity. The article builds on this foundation to provide an intuitive understanding of the Dirac delta function as the limit of a normalized Gaussian, and applies Laplace transforms to solve the differential equation. The proposed interpretation helps bridge the gap between abstract mathematical concepts and physical intuition, offering a meaningful way for students to grasp solutions involving the Dirac delta. [ABSTRACT FROM AUTHOR] |
| Abstract (Portuguese): |
Este artículo presenta una estrategia didáctica para apoyar a los estudiantes en la comprensión del problema de valor inicial 𝜹(t), v(0) = 0: y su solución v(t) = 1, donde la Delta de Dirac 𝜹(t) aparece como parte de la ecuación diferencial. La propuesta consiste en interpretar el problema en términos de una situación física que involucra a una partícula inicialmente en reposo, sometida a una fuerza impulsiva. Mediante el análisis de un problema elemental de la mecánica clásica--en el que una fuerza conocida actúa durante un intervalo de tiempo finito--los estudiantes pueden comprender el papel del impulso y cómo este se traduce en un cambio de velocidad. A partir de esta base, se ofrece una interpretación intuitiva de la función delta de Dirac como el límite de una gaussiana normalizada, y se aplica la transformada de Laplace para resolver la ecuación diferencial. La interpretación propuesta ayuda a cerrar la brecha entre conceptos matemáticos abstractos y la intuición física, ofreciendo una forma significativa para que los estudiantes comprendan soluciones que involucran a la delta de Dirac. [ABSTRACT FROM AUTHOR] |
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| Database: |
Education Research Complete |
