Cette œuvre pr�sente les bases th�oriques, les transformations et les m�thodes permettant de r�duire une forme Pfaffienne � une forme canonique simple, tout en �clairant le lien entre int�grales g�n�rales et int�grales singuli�res.

� travers une progression claire, le livre explore les notions cl�s : multiplicit�s, �l�ments lin�aires, et le r�le des �quations aux d�riv�es partielles dans l’�tude des int�grales. On y voit comment changer de variables, ramener des expressions � des formes normales et comprendre les conditions qui garantissent l’existence d’int�grales de Pfaff dans diff�rents cas.

Descriptions des formes Pfaffiennes et des conditions d’int�grabilit�.
Techniques de r�duction � des formes canoniques et exposition de cas particuliers.
Liens entre les m�thodes historiques (Pfaff, Monge, Cartan) et les d�veloppements modernes.
Applications th�oriques menant jusqu’aux �quations aux d�riv�es partielles et � leurs int�grales.

Id�al pour les lecteurs curieux des fondements des m�thodes d’int�gration et de l’histoire des �quations diff�rentielles.

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