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

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 On the basis of Liouville's unpublished notes the book reconstructs Liouville's hitherto unknown theories of stability of rotating masses of fluid, potential theory, Galois theory and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.

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Content:
Front Matter....Pages i-xix
Front Matter....Pages 1-1
Youth (1809–1830)....Pages 3-23
Climbing the Academic Ladder (1830–1840)....Pages 25-68
Professor, Academician, and Editor (1840–1848)....Pages 69-147
The Second Republic (1848–1852)....Pages 149-174
The Last Flash of Genius (1852–1862)....Pages 175-225
Old Age (1862–1882)....Pages 227-260
Front Matter....Pages 261-261
Juvenile Work....Pages 263-301
Differentiation of Arbitrary Order....Pages 303-349
Integration in Finite Terms....Pages 351-422
Sturm-Liouville Theory....Pages 423-475
Figures of Equilibrium of a Rotating Mass of Fluid....Pages 477-512
Transcendental Numbers....Pages 513-526
Doubly Periodic Functions....Pages 527-557
Galois Theory....Pages 559-580
Potential Theory....Pages 581-635
Mechanics....Pages 637-708
Geometry....Pages 709-755
Back Matter....Pages 757-885

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Content:
Front Matter....Pages i-xix
Front Matter....Pages 1-1
Youth (1809–1830)....Pages 3-23
Climbing the Academic Ladder (1830–1840)....Pages 25-68
Professor, Academician, and Editor (1840–1848)....Pages 69-147
The Second Republic (1848–1852)....Pages 149-174
The Last Flash of Genius (1852–1862)....Pages 175-225
Old Age (1862–1882)....Pages 227-260
Front Matter....Pages 261-261
Juvenile Work....Pages 263-301
Differentiation of Arbitrary Order....Pages 303-349
Integration in Finite Terms....Pages 351-422
Sturm-Liouville Theory....Pages 423-475
Figures of Equilibrium of a Rotating Mass of Fluid....Pages 477-512
Transcendental Numbers....Pages 513-526
Doubly Periodic Functions....Pages 527-557
Galois Theory....Pages 559-580
Potential Theory....Pages 581-635
Mechanics....Pages 637-708
Geometry....Pages 709-755
Back Matter....Pages 757-885
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