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7.4 Cauchy-Euler Equation - University of Utah
www.math.utah.eduThe di erential equation a nx ny(n) + a n 1x n 1y(n 1) + + a 0y = 0 is called the Cauchy-Euler di erential equation of order n. The sym-bols a i, i = 0;:::;n are constants and a n 6= 0. The Cauchy-Euler equation is important in the theory of linear di er-ential equations because it has direct application to Fourier’s method
Electromagnetism: the simplest gauge theory
www.physics.usu.edu* It can be shown using techniques from the inverse problem of the calculus of variations that there is no variational principle for Maxwell’s equations built solely from (E;~ B~) and ... Show that the EL derivative of the Maxwell Lagrangian satis es the di er-ential identity D E ... on any di erential form, d2 = 0. It is easy to check all ...