New PDF release: Collected Works of Charles François Sturm

By Jean-Claude Pont, Isaac Benguigui (auth.), Prof. Jean-Claude Pont (eds.)

ISBN-10: 3764379898

ISBN-13: 9783764379896

ISBN-10: 3764379901

ISBN-13: 9783764379902

Charles François Sturm was once born in Geneva, Switzerland, on September 29, 1803. He got his medical schooling during this urban and commenced his wealthy medical profession there via major study in sound propagation and compressibility of fluids. In September of 2003, at the get together of the 2 hundredth anniversary of his beginning, his domestic urban honoured his around the globe attractiveness with a colloquium and workshop below the sponsorship of the college of Geneva.

This quantity is predicated on lectures provided at that colloquium, which concerned about C.F. Sturm's personal paintings. The publication incorporates a number of reproductions of his medical courses. Sturm contributed significantly to geometry (theory of polygons, simple geometry, projective geometry, conic sections), algebra, research (differential equations, series), optics (caustics, physiological optics), mechanics, and different parts of physics (particularly fluid mechanics and pace of sound in water).

These unique papers are followed via contributions from the world over popular specialists who've labored on and deepened realizing of many subject matters of curiosity to Sturm, specifically differential equations, optics and algebraic curves. the amount enhances the e-book Sturm-Liouville concept. previous and Present (ISBN 978-3-7643-7066-4) that still originates from that colloquium.

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Extra resources for Collected Works of Charles François Sturm

Sample text

Sturm, C. 1837b.

Berman 1979, 13]. Sturm’s published sketch of a proof actually shows that he anticipated the Perron–Fröbenius theorem in a special case. Sturm denoted the real zeros of the quintic Q (which is, as we saw above, the determinant of the matrix Ar + B) by α, β, γ, δ, ε with α being the largest, etc. , the matrix Aα + B has non-positive off-diagonal entries), then the components of the eigenvector corresponding to the generalized eigenvalue α (can be chosen to have) all have the same sign. A similar result holds [clearly] if Gij (α) ≥ 0.

Its connection to Sturm’s theorem It is conspicuous that Sturm’s original ideas on Sturm–Liouville theory were presented to the Académie des Sciences a few weeks after he had presented his famous theorem concerning the real roots of polynomial equations [Sturm 1829a]. This seems to suggest that there was a connection between the development of the two theories. Historically they have a common root in the works of Fourier. However, there are even mathematical similarities that may suggest a common mathematical origin.

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Collected Works of Charles François Sturm by Jean-Claude Pont, Isaac Benguigui (auth.), Prof. Jean-Claude Pont (eds.)

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