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In this paper the theory of jets based on Weil's near points is applied to Lie equations and pseudogroups. Linear systems of partial differential equations are interpreted, in a canonical way, as distributions on the fibre bundles of invertible jets invariant under translations. We prove the two fundamental theorems for Lie equations and generalize the results of Rodrigues; a geometric correspondence between linear and nonlinear Lie equations is given, and the symbols of a linear Lie equation and its prolongations are canonically identified with the symbols of their attached nonlinear equations. From this fact we deduce that a linear Lie equation verifies the conditions of Goldsmichmidt's criterion on formal integrability if and only if its attached nonlinear Lie equation satisfies them locally. Finally, we define the Cartan 1-form on the fibre bundle of invertible jets and give a global form to the equivalence between the Lie and Cartan definitions of continuous groups. ᮊ

In this paper we apply Weil bundle techniques to the study of formal integrability for systems of nonlinear partial differential equations. We clarify the role of the curvature and show that both the statement and proof of Goldschmidt's criterion on formal integrability are of algebraic nature. This fact allows us to obtain a version of this theorem which holds for smooth, algebraic, or analytic manifolds. Finally, we give a definition for the characteristic co-vectors of a system of partial differential equations and how their relationship with the Cauchy᎐Kowalevski normal form. ᮊ

The main goal of this work is to present the method designed and put into practice by the Department of Mathematics at I.E.S Norba Caesarina for creating digital books (e-books) in EPUB 3 format, including videos and MathML. The natural way of generating the XHTML code for creating the EPUB 3 is to use LaTex for editing the final text, transforming it into XHTML. We also show how can reproduce in EPUB 3, external videos stored in YouTube; how generate SVG images from GeoGebra and implement questionnaires in EPUB 3 without JavaScript knowledge, preserving the accessibility associated with MathML equations.