CiNii 図書 - Mathematische Werke : herausgegeben unter Mitwirkung einer von der königlichen preussischen Akademie der Wissenschaften eingesetzten Commission

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.

Vorwort
1. Ueber die Entwiklung der Modular-Functionen
2. Darstellung einer analytischen Function einer complexen Veranderlichen, deren absoluter Betrag zwischen zwei gegebenen Grenzen liegt
3. Zur Theorie der Potenzreihen
4. Definition analytischer Functionen einer veranderlichen vermittelst algebraischer Differentialgleichungen
5. Bemerkungen uber die analytischen Facultaten
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 Facultaten
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 geodatischen Linien auf dem dreiaxigen Ellipsoid
15. Bemerkungen uber die Integration der hyperelliptischen Differentialgleichungen
16. Zur Integration der linearen partiellen Differentialgleichungen mit constanten Coefficienten
17. Theorie der Abel'schen Functionen.

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 2 was published in 1895.

1. Ueber eine Gattung reell periodischer Functionen
2. Zur Theorie der bilinearen und quadratischen Formen
3. Ueber die allgemeinsten eindeutigen un 2n-fach periodischen Functionen von n Veranderlichen
4. Ueber das sogenannte Dirichlet'sche Princip
5. Neuer Beweis eines Hauptsatzes der Theorie der periodischen Functionen von mehreren Veranderlichen
6. Ueber continuirliche Functionen eines reellen Arguments
7. Bemerkungen zur Integration eines Systems linearer Differentialgleichungen mit constanten Coefficienten
8. Zur Theorie der eindeutigen analytischen Functionen
9. Untersuchngen uber die 2r-fach periodischen Functionen von r Veranderlichen
10. Einige auf die Theorie der analytischen Functionen mehrerer Veranderlichen sich beziehende Satze
11. Ueber einen functionstheoretischen Satz des Herrn G. Mittag-Leffler
12. Zur Functionslehre
13. Aus einem bisher noch nicht veroeffentlichten Briefe an Herrn Prof. Schwarz
14. Zur Theorie der elliptischen Functionen
15. Zur Theorie der elliptischen Functionen
16. Zur Theorie der aus n Haupteinheiten gebildeten complexen Groessen
17. Zu Lindemann's Abhandlung: 'Ueber die Ludolph'sche Zahl'
Anmerkung.

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. Edited by Johannes Knoblauch (1855-1915), Volume 3 was published in 1903.

Vorwort
1. Ueber die analytische Darstellbarkeit sogenannter willkurlicher Functionen reeller Argumente
2. Untersuchungen uber die Flachen, deren mittlere Krummung uberall gleich Null ist
3. Allgemeine Untersuchungen uber 2n-fach periodische Functionen von n Veranderlichen
4. Ueber die Convergenz der Theta-Reihen beliebig vieler Argumente
5. Verallgemeinerung einer Jacobi'schen Thetaformel
6. Nachtrag zu der am 4. Marz 1858 in der koenigl. Akademie der Wissenschaften gelesenen Abhandlung
7. Ueber die Bedingungen der Zerlegbarkeit einer ganzen rationalen Function von mehr als zwei Veranderlichen
8. Zur Theorie der Jacobi'schen Functionen von mehreren Veranderlichen
9. Rein geometrischer Beweis des Hauptsatzes der projectivischen Geometrie
10. Zur Dioptrik
11. Zwei specielle Flachen vierter Ordnung
12. Ueber eine die Raumcurven constanter Krummung betreffende, von Delaunay herruhrende Aufgabe der Variationsrechnung
13. Fortsetzung der Untersuchung uber die Minimalflachen
14. Analytische Bestimming einfach zusammenhangender Minimalflachenstucke
15. Ueber eine besondere Gattung von Minimalflachen
16. Einfacher Beweis eines Hermitischen Satzes
17. Neuer Beweis des Satzes, dass jede ganze rationale Function einer Veranderlichen dargestellt werden kann als ein Product aus linearen Functionen derselben Veranderlichen
18. Zur Determinantentheorie
19. Zur Theorie der hyperelliptischen Functionen
20. Ueber Normalformen algebraischer Gebilde
21. Zur Integration der hyperelliptischen Differentialgleichungen
Anhang
Anmerkung.

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. Edited by Johannes Knoblauch (1885-1915) and Georg Hettner (1854-1914), Volume 4 was published in 1902.

Vorwort
Einleitung
Part I. Algebraische Grundlage der Theorie
Part II. Die Abelschen Integrale
Part III. Die Abelschen Functionen
Alphabetisches Inhalts-Verzeichniss
Bemerkungen und Berichtigungen.

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. Edited by Johannes Knoblauch (1855-1915), Volume 5 was published in 1915.

Vorwort
Einleitung
1. Transformation des Differentials
2. Integration der Differentialgleichung durch Reihenentwicklung
3. Die Function
4. Die Function
5. Die partielle Differentialgleichung der Function
6. Loesung der Gleichung durch Reihenentwicklung
7. Bestimmung aller Loesungen der Gleichung
8. Grundformeln der Theorie der Function
9. Die Perioden der Function fur reelle Invarianten
10. Die Functionen und die Quotienten
11. Die Differentialgleichungen der Quotienten
12. Darstellung der Function durch ein unednliches Product
13. Umwandlung des unendlichen Productes fur die Function
14. Darstellung elliptischer Functionen mittels der Function
15. Darstellung elliptischer Functionen durch der Function
16. Darstellung der Functionen durch unendliche Producte
17. Weitere Umwandlung der Productsausdrucke fur die Functionen
18. Die vier Theta-Functionen
19. Die allgemeine Theta-Functionen
20. Die Theta-Functionen mit zwei Parametern
21. Beziehungen zwischen Functionen von mehrgliedrigen Argumenten
22. Die Additionstheoreme der Quotienten
23. Das Multiplicationstheorem der Function
24. Das Multiplicationstheorem der Quotienten
25. Die elliptischen Integrale
26. Die Additionstheoreme der Integrale erster, zweiter und dritter Art
27. Formeln zur Berechnung der Perioden
28. Bestimmung eines primitiven Periodenpaares der Function fur beliebige Groessen
29. Bestimmung von u aus der Gleichung
30. Anwendung der Formeln des achtzehnten und neunundzwanzigsten Kapitels auf den Fall reeller Invarianten
31. Transformation der elliptischen Functionen
32. Transformation specieller Functionen
33. Zur Transformation der Function
34. Die Transformation zweiter Ordnung
Alphabetisches Inhalts-Verzeichniss.

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. Edited by Rudolf Rothe (1873-1942), Volume 6 was published in 1915.

Vorwort
Einleitung
Part I. Der Flacheninhalt des Mantels einers schiefen Kegels mit kreisfoermiger Grundflache
Part II. Die Oberflache eines dreiaxigen Ellipsoids
Part III. Das Potential eines homogenen Ellipsoids und einer homogenen Ellipse
Part IV. Bestimmung des Intervalls fur den Werth des Integrals
Part V. Integration der elliptischen Differentialgleichung
Part VI. Die Theilung der Lemniscate und die complexe Multiplication der elliptischen Functionen
Part VII. Das spharische und das ebene Pendel
Part VIII. Die Bewegung eines starren Koerpers um einen festen Punkt
Part IX. Bestimmung der geodatischen Linien auf einem Rotationsellipsoide
Anmerkungen.

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. Edited by Rudolf Rothe (1873-1942), Volume 7 was published in 1927.

Vorwort
Einleitung
Part I. Theorie der Maxima und Minima von Functionen einer und mehrerer Veranderlichen
Part II. Variationsrechnung
Anmerkung
Berichtigungen
Alphabetisches Inhalts-Verzeichniss.

Mathematische Werke : herausgegeben unter Mitwirkung einer von der königlichen preussischen Akademie der Wissenschaften eingesetzten Commission

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