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Zbl 0949.01001
Gray, Jeremy J.
Linear differential equations and group theory from Riemann to Poincaré. 2nd ed. (English)
[B] Boston, MA: Birkhäuser. xx, 338 p. \$ 64.95 (2000). ISBN 0-8176-3837-7/hbk

This volume is a second edition of [Linear differential equations and group theory from Riemann to Poincaré (1984; Zbl 0536.01013)].\par The previous edition has been reviewed very favorably. Some extensions are provided here.\par Since 1986, the Riemann-Hilbert problem has been shown not to be solvable in general and a counterexample is provided.\par Appendix six gives an account of the Picard-Vessiot theory (a Galois theory for ODEs) up to the early 1900s.\par Appendix seven presents the work of Appel and Goursat on the hypergeometric equation.\par The point of view of Poincaré for solving ODEs is developed and implications are highlighted. Three texts of Poincaré (1880) are commented.\par This book can only enrich a scientific library.
[A.Akutowicz (Berlin)]

MSC 2000:: *01-02 Research monographs (history)
01A55 Mathematics in the 19th century
34-03 Historical (ordinary differential equations)
20-03 Historical (group theory)

Keywords: linear differential equations; Abelian integrals; theta functions; hypergeometric series; Jacobi; Kummer; Riemann; Fuchs; Schwarz; Klein; Jordan; Hermite; Dedekind; Betti; Kronecker; Gordon; Picard-Vessiot theory; hypergeometric equation

Citations: Zbl 0536.01013

Cited in: Zbl 1141.01010

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	Scientific prize winners of the ICM 2010
	Overhang
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