Joseph Liouville 1809–1882: Master of Pure and Applied MathematicsSpringer Science & Business Media, 6 de des. 2012 - 885 pàgines 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 On the basis of Liouville's unpublished notes the book reconstructs Liouville's hitherto unknown theories of stability of rotating masses of fluid, potential theory, Galois theory and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. |
Continguts
3 | |
25 | |
Defeats at the Académie and at the École Polytechnique | 41 |
Liouville and Dirichlet against Libri | 59 |
Professor Academician and Editor 18401848 | 69 |
Collège 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 Collège de France | 165 |
Lectures at the Collège de France | 171 |
Ernest Liouville Statistics Bienaymè 18521853 | 177 |
Friendship with Dirichlet | 185 |
Sturms Death | 194 |
Courses at the Collège 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 Ampères Force Law 757 | 759 |
The Sketch of Contents of Liouvilles | 767 |
Bibliography | 789 |
813 | |
855 | |
Altres edicions - Mostra-ho tot
Joseph Liouville 1809–1882: Master of Pure and Applied Mathematics Jesper Lützen Visualització de fragments - 1990 |
Joseph Liouville 1809–1882: Master of Pure and Applied Mathematics Jesper Lützen Previsualització no disponible - 2013 |
Joseph Liouville 1809–1882: Master of Pure and Applied Mathematics Jesper Lützen Previsualització no disponible - 2011 |
Frases i termes més freqüents
Abel Abel's Académie des Sciences algebraic functions Ampère Ampère's Arago arbitrary argument Bureau des Longitudes Cauchy Cauchy's Chapter Chasles coefficients Collège de France Comptes Rendus constant convergence coordinates curvature derivative differential equations Dirichlet discussed doubly periodic functions École Polytechnique eigenfunctions eigenvalues elliptic functions elliptic integrals equilibrium expression fact finite terms forme x² formula Fourier series fractional calculus Galois Galois's Gauss geodesic geometry heat Hermite ideas integration in finite Jacobi ellipsoid Lagrange Lamé Lamé functions Laplace later lectures letter Libri Liou Liouville wrote Liouville's Journal Liouville's theorem mathematical mathematicians memoir method Neuenschwander 1984a nombres premiers notebooks obtained paper Paris particular Poincaré Poisson polynomial problem proof Proposition proved published rational functions remark roots Serret solution solved Sturm Sturm-Liouville theory surface Théorème Thomson tion Toul transcendental variables Verrier zero