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Vorlesungen Über Höhere Mathematik: Gewöhnliche Und Partielle Differentialgleichungen. Variationsrechnung. Funktionen Einer Komplexen Veränderlichen

by Adalbert Duschek
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Book cover type: Paperback
  • ISBN13: 9783709176887
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 513
  • Original Price: EUR 70.08
  • Language: German
  • Edition: Softcover Repri
  • Item Weight: 840 grams
  • BISAC Subject(s): General

die ernst genommen sein will, an KAMKES Arbeit einfach nicht vorbeigehen kann, auch dann nicht, wenn sie sich ein wesentlich anderes Ziel gesetzt hat. Dazu kommt, daB ich - bedingt durch den Plan des ganzen Werkes - zwangUiufig zur selben Beschrankung des Stoffes im GroBen komme, die sich KAMKE frei- willig gibt: Zur Beschrankung auf das Reelle und auf die Diskussion von Anfangs- wertaufgaben; Randwertaufgaben werden nur gelegentlich gestreift und an einzelnen Beispielen, am haufigsten naturlich in der Variationsrechnung, be- handelt. Aber KAMKE hat sein Buch fur den Mathematiker geschrieben; dem Physiker bringt es zu viel - an minuzioser Strenge - und zugleich zu wenig: Es ist wohl fast selbstverstandlich, daB ich beispielsweise den Begriff des all- gemeinen Integrals nicht vollig unter den Tisch fallen lassen konnte und bei den partiellen Differentialgleichungen erster Ordnung die Theorie des vollstandigen Integrals sogar ziemlich ausfiihrlich bringen muBte. In dem Ahschnitt uber Variationsrechnung habe ich mich grundsatzlicb mit der Diskussion der notwendigen Bedingungen begnugt, obwohl yom Hilbertschen Un- abhangigkeitssatz nur mehr ein verhaltnismaBig kleiner Schritt zu den hinreichen- den Bedingungen von WEIERSTRASS gefuhrt hatte. Ziemlich ausfiihrlich und bis zu einem gewissen AbschluB sind die Extremalenfelder und die Hamilton-J akobische Theorie behandelt. Ein kleiner Exkurs uber allgemeine Koordinaten und den Rie- mannschen Raum, im wesentlichen aus der Tensorrechnung von A. HOCHRAINER und mir ubernommen, hat sich hier halbwegs zwanglos einfiigen lassen. Dber den letzten Abschnitt, die Funktionentheorie, ist wenig zu sagen.

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