Joseph Liouville 1809–1882: Master of Pure and Applied Mathematics

Portada
Springer Science & Business Media, 6 de des. 2012 - 885 pŕgines
This scientific biography of the mathematician Joseph Liouville is divided into two parts. The first part is a chronological account of Liouville's career including a description of the institutions he worked in, his relations with his teachers, colleagues and students, and the historical context of his works. It portrays the French scientific community in a period when Germany and England had surpassed France as the leading nations in mathematics and physics. The second part of the book gives a detailed analysis of Liouville's major contributions to mathematics and mechanics. The gradual development of Liouville's ideas, as reflected in his publications and notebooks, are related to the works of his predecessors and his contemporaries as well as to later developments in the field. On the basis of Liouville's unpublished notes the book reconstructs Liouville's hitherto unknown theories of stability of rotating masses of fluid, potential theory, Galois theory and electrodynamics. It also incorporates valuable added information from Liouville's notes regarding his works on differentiation of arbitrary order, integration in finite terms, Sturm-Liouville theory, transcendental numbers, doubly periodic functions, geometry and mechanics.
 

Quč opinen els usuaris - Escriviu una ressenya

No hem trobat cap ressenya als llocs habituals.

Continguts

Youth 18091830
3
Climbing the Academic Ladder 18301840
25
Defeats at the Académie and at the École Polytechnique
41
Liouville and Dirichlet against Libri
59
Professor Academician and Editor 18401848
69
Collčge de France
82
Académie des Sciences
92
The Bureau des Longitudes
98
Conclusion
420
The Roots of SturmLiouville Theory
426
Sturms First Memoir
435
Sturms Second Memoir
443
Liouvilles Mature Papers on SecondOrder Differential Equations
451
Liouvilles Generalization of SturmLiouville Theory
460
Concluding Remarks
472
Jacobi Ellipsoids
479

Guiding Young Talents
104
Hermite Bertrand and Serret
116
Foreign Visitors
132
A Coherent Mathematical Universe
146
Revolution
153
Member of the Constituting Assembly
158
The Second Election at the Collčge de France
165
Lectures at the Collčge de France
171
Ernest Liouville Statistics Bienaymč 18521853
177
Friendship with Dirichlet
185
Sturms Death
194
Courses at the Collčge de France
201
Great Teaching LoadNo Research
207
Liouvilles Final Opinion of Cauchy
213
Declining Influence in the Académie Bour
223
Lecturer and Promoter
232
The FrancoPrussian War and the Commune
240
The Last Courses
247
Longing for Death
255
Juvenile Work
262
Theory of Heat
281
Differential Equations
293
Differentiation of Arbitrary Order
303
Foundations
320
Fractional Differential Equations
332
Rigor
342
Integration in Finite Terms 351
348
Abels Contributions
358
Integration in Algebraic Terms
369
Integration in Finite Terms
382
Solution of Differential Equations in Finite Terms
401
Further Developments
411
Methods and Proofs
489
Concluding Remarks
509
Liouville on the Transcendence of e 1840
516
The Impact of Liouvilles Discovery
525
The Discovery of Liouvilles Theorem
534
The Gradual Development of the General Theory
544
The Final Form of Liouvilles Theory
550
Galois Theory 559
558
Liouvilles Commentaries
567
Liouvilles Publication of the Works of Galois
576
Liouvilles Published Contributions
589
Liouville on Potentials of Ellipsoids
595
Liouvilles Unpublished Notes on Spectral Theory of Integral
601
Poincarés Fundamental Functions
629
Mechanics
637
Celestial Mechanics
643
Liouvilles Theorem on the Volume in Phase Space
657
Rational Mechanics
665
Poisson on Liouvilles Theorem
673
Liouvilles Lecture on Mechanics
679
Liouvilles Unpublished Notes Generalized Poisson Brackets
686
The Liouvillian Integrable Systems
700
Concluding Remarks
706
Relations with Mechanics and Elliptic and Abelian Functions
716
Inversion in Spheres William Thomsons Influence
727
Contributions to Gaussian Differential Geometry
739
Liouville on Ampčres Force Law 757
767
Bibliography
789
Other References
813
Index
855
Copyright

Altres edicions - Mostra-ho tot

Frases i termes més freqüents

Informació bibliogrŕfica