"Cartan's work provides a superb text for an undergraduate course in advanced calculus, but at the same time it furnishes the reader with an excellent foundation for global and nonlinear algebra."—Mathematical Review
"Brilliantly successful."—Bulletin de l'Association des Professeurs de Mathematiques
"The presentation is precise and detailed, the style lucid and almost conversational . . . clearly an outstanding text and work of reference."—Annales
Cartan's Formes Differentielles was first published in France in 1967. It was based on the world-famous teacher's experience at the Faculty of Sciences in Paris, where his reputation as an outstanding exponent of the Bourbaki school of mathematics was first established.
Addressed to second- and third-year students of mathematics, the material skillfully spans the pure and applied branches in the familiar French manner, so that the applied aspects gain in rigor while the pure mathematics loses none of its dignity. This book is equally essential as a course text, as a work of reference, or simply as a brilliant mathematical exercise.
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Banach space bilinear calculate canonical form change of variable Chap class C1 compact set condition consider constant contained continuous function continuous mapping coordinates Darboux frame deﬁned deﬁnition denote derivative differential equation differential form Diﬁrential Calculus element equal exists exterior product extremal ﬁeld of frames ﬁnd ﬁnite number ﬁrst ﬁxed form of degree formula function f function of class geodesic curvature geodesic torsion given Lemma linear mapping M E S mapping of class multilinear alternating normal curvature notation obtain open neighbourhood open set open subset orthogonal orthonormal frames parametrization partition of unity path permutation piecewise of class plane Prop PROPOSITION prove quadratic form rectangle relative minimum right-hand side satisﬁes scalar set with boundary solution starlike with respect subspace suﬂicient supp suppose surface tangent vector theory total curvature transformation umbilical point values in F vanishes variety vector space