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By Forster Otto

Der vorliegende Band stellt den dritten Teil eines Analysis-Kurses für Studenten der Mathematik und Physik dar und behandelt die Integralrechnung im $R^n$ mit Anwendungen. In einem ersten Teil wird das Lebesguesche necessary im $R^n$ eingeführt und es werden die wichtigsten Sätze dieser Theorie bewiesen. Als Anwendungen werden u.a. die $L_p$-Räume und die Fouriertransformation behandelt. Als nächstes wird der Gaußsche Integralsatz bewiesen, der dann zum Studium der Potentialgleichung und zur Konstruktion von Fundamental-Lösungen einiger anderer partieller Differentialgleichungen benützt wird. In einem letzten Teil wird schließlich der Differentialformenkalkül eingeführt. Dieser Teil enthält auch eine Theorie der Kurvenintegrale sowie den allgemeinen Stokesschen Integralsatz für Untermannigfaltigkeiten des R^n mit Anwendungen auf die Integralsätze für holomorphe Funktionen einer und mehrerer Variablen.

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Analysis 3 by Forster Otto

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