Leçons sur les invariants intégraux

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[English translation](https://isidore.co/calibre/#panel=book_details&book_id=7585)cites Lie's "[Über Integralinvarianten und Differentialgleichungen](https://isidore.co/calibre/#panel=book_details&book_id=7404)"* * *[MR1560686](https://mathscinet.ams.org/mathscinet-getitem?mr=1560686)The theory of integral invariants was first set forth by H. Poincaré in the third volume of *Les Méthodes Nouvelles de la Mécanique Céleste.* Cartan develops this theory systematically in his Leçons, using a different point of view. Instead of connecting an integral invariant with a system of differential equations as did Poincaré, Cartan considers the integrand of this integral as a differential form and studies its properties of invariance under a group of transformations.The mathematician will be especially interested to read this book because of the elegant treatment of the subject. Enough of the classical theories of differential forms and continuous groups, for instance, is given to make the book readable. Considerable space is devoted to the development of methods of deriving integral invariants, such as Jacobi's last multiplier and infinitesimal transformations.These Leçons are to be recommended to students of applied mathematics because of the admirable treatment of physical problems from the modern point of view. The theory of turbulence, the *n* -body problem, and certain problems in optics are considered from the point of view of tensors and their relation to the integral invariant theory.E. P. LANEH. T. DAVIS