Differential Equations -Not Just a Bag Tricks!

• Autores: Shirley Llamado Yap
• Localización: Mathematics magazine, ISSN 0025-570X, Vol. 83, Nº. 1, 2010, págs. 3-14
• Idioma: inglés
• DOI: 10.4169/002557010x479947
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• Resumen

  • Differential equations often seems like a hodgepodge of techniques designed to solve very specific equations. There is, however, a unifying theme for many of those techniques, which is to find the right coordinate system with which to express the equation. In the mid-nineteenth century, Sophus Lie discovered how to unify and extend many of the techniques that existed at his time by using the symmetries of differential equations to find good coordinate systems. This paper explains the symmetry method at a level suitable for undergraduates who have taken vector calculus and differential equations.