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Full Description
The German mathematician Karl Weierstrass (1815-97) is generally considered to be the father of modern analysis. His clear eye for what was important is demonstrated by the publication, late in life, of his polynomial approximation theorem; suitably generalised as the Stone-Weierstrass theorem, it became a central tool for twentieth-century analysis. Furthermore, the Weierstrass nowhere-differentiable function is the seed from which springs the entire modern theory of mathematical finance. The best students in Europe came to Berlin to attend his lectures, and his rigorous style still dominates the first analysis course at any university. His seven-volume collected works in the original German contain not only published treatises but also records of many of his famous lecture courses. Volume 1 was published in 1894.
Contents
Vorwort; 1. Ueber die Entwiklung der Modular-Functionen; 2. Darstellung einer analytischen Function einer complexen Veränderlichen, deren absoluter Betrag zwischen zwei gegebenen Grenzen liegt; 3. Zur Theorie der Potenzreihen; 4. Definition analytischer Functionen einer veränderlichen vermittelst algebraischer Differentialgleichungen; 5. Bemerkungen über die analytischen Facultäten; 6. Reduction eines bestimmten dreifachen Integrals; 7. Beitrag zur Theorie der Abel'schen Integrale; 8. Zur Theorie der Abel'schen Functionen; 9. Ueber die Theorie der analytischen Facultäten; 10. Akademische Antrittsrede; 11. Ueber die Integration algebraischer Differentiale vermittelst Logarithmen; 12. Ueber ein die homogenen Functionen zweiten Grades betreffendes Theorem; 13. Neuer Beweis des Fundamentalsatzes der Algebra; 14. Ueber die geodätischen Linien auf dem dreiaxigen Ellipsoid; 15. Bemerkungen über die Integration der hyperelliptischen Differentialgleichungen; 16. Zur Integration der linearen partiellen Differentialgleichungen mit constanten Coefficienten; 17. Theorie der Abel'schen Functionen.
