Bendixson Ivar Otto (1 results)
Published by Kongl. Vetenskaps-Akademiens, Stockholm 1892
- Softcover
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Soft cover. Condition: Very Good. 11 pamphlets, 8vo; all in original plain wrappers, four papers inscribed by Bendixson 'M. J. Tannery hommage respecteuse de l'auteur'. FIRST EDITIONS, OFFPRINTS FROM ÖFVERSIGT AF KONGL. VETENSKAPS-AKADEMIENS FÖRFHANDLINGAR, OF THESE PAPERS ON DIFFERENTIAL EQUATIONS. 'Bendixson is probably best r…emembered for the Poincaré-Bendixson theorem. We shall say a little about how Bendixson came to prove this result. This came about because of his work in real analysis. In this area he first studied uniform convergence of series of real functions and took an important step towards giving precise conditions when the limit function of continuous functions is continuous. In examining periodic solutions of differential equations Bendixson used methods based on continued fractions. These methods had first been used by Legendre to prove that e and ? are irrational. 'The analysis problem which intrigued Bendixson more than all others was the investigation of integral curves to first order differential equations, in particular he was intrigued by the complicated behaviour of the integral curves in the neighbourhood of singular points. This important problem was first studied by Briot and his friend Bouquet and, before Bendixson worked on it, had recently been investigated by Poincaré. Poincaré had obtained a qualitative description of the integral curves but it was Bendixson who gave a quantitative description near the singular points' (MacTutor History of Mathematics). Provenance: Presentation inscriptions by Bendixson to Jules Tannery (1848-1910) on four of the papers. 'Tannery studied under Charles Hermite and was the PhD advisor of Jacques Hadamard. Under Hermite, he received is doctorate in 1874 for his thesis Propriétés des Intégrales des Équations Différentielle Linéaires à Coefficients Variables. He discovered a surface of the fourth order of which all the geodesic lines are algebraic. He was not an inventor, however, but essentially a critic and methodologist. He once remarked, "Mathematicians are so used to their symbols and have so much fun playing with them, that it is sometimes necessary to take their toys away from them in order to oblige them to think." He notably influenced Paul Painlevé, Jules Drach, and Émile Borel to take up science. His efforts were mainly directed to the study of the mathematical foundations and of the philosophical ideas implied in mathematical thinking' (Wikipedia).