Anwendungsorientierte Mathematik: Vorlesungen Und Übungen Für Studierende Der Ingenieur- Und Wirtschaftswissenschaften
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Das in den ersten beiden Auflagen bewahrte Konzept einer Einfiihrung in die Differen- tialrechnung wurde auch in der dritten Auflage beibehalten. Studenten der Ingenieur- oder Wirtschaftswissenschaften, aber auch der im Beruf stehende Praktiker, beno- tigen eine methodisch orientierte Darstellung, die sich inhaltlich an den Anwendun- gen der Mathematik in diesen Bereichen ausrichtet. Das schlieBt theoretische Uber- legungen nicht aus, beschrankt diese jedoch auf jenes MaB, das fiir das Verstandnis des Infinitesimalkalkiils unbedingt erforderlich ist. Nach wie vor haben die Studierenden des ersten Semesters enorme Schwierigkeiten beim Ubergang von der Schule zur Hochschule. Hier will dieses Buch eine Briicke schlagen, indem es der eigentlichen Differentialrechnung ein ausfiihrlich gehaltenes Kapitel iiber reelle Funktionen voranstellt. Dabei werden die wichtigsten Klassen ele- mentarer Funktionen von den Polynomen bis zu den Hyperbelfunktionen behandelt und die fiir den Anwender interessanten Eigenschaften herausgehoben. Ein weiteres Kapi- tel iiber komplexwertige Funktionen eines reellen Parameters fiihrt in die wichtigsten Ortskurven der GauBschen Zahlenebene ein, die vornehmlich in der Regelungstechnik benotigt werden. Wichtigste Erweiterung gegeniiber der zweiten Auflage ist die Erganzung jedes Teil- abschnitts urn Ubungsaufgaben. Diese sind nach Anzahl, Umfang und Schwierigkeits- grad so bemessen, daB sie vom Leser in einem vertretbaren Zeitraum bearbeitet werden konnen und ihm eine Vorstellung vom Lehrziel des entsprechenden Abschnitts vermitteln. Zur Selbstkontrolle sind die Losungen, in vielen Fallen mit Zwischen- ergebnissen und Herleitungen, im Anhang aufgefiihrt.
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