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Differentialgleichungen erster Ordnung

In: Eine Einführung in gewöhnliche Differentialgleichungen

Author

Listed:
  • Martin Hermann

    (Friedrich Schiller University, Institute of Applied Mathematics)

  • Masoud Saravi

    (Shomal University, Department of Technical and Engineering)

Abstract

Zusammenfassung Das Kapitel 2 befasst sich mit skalaren Differentialgleichungen erster Ordnung. Die Existenz und Eindeutigkeit von Lösungen von Anfangswertproblemen wird auf der Grundlage der bekannten Theoreme von Peano und Picard-Lindelöf untersucht. Die analytischen Standardtechniken zur Bestimmung der exakten Lösung werden beschrieben. Darüber hinaus wird die Lösung von Differentialgleichungen erster Ordnung hohen Grades (Clairaut- und Lagrange-Gleichung), die häufig in den Anwendungen auftreten, diskutiert. Das Kapitel endet mit der Diskussion über Kurvenfamilien und orthogonale Trajektorien.

Suggested Citation

  • Martin Hermann & Masoud Saravi, 2024. "Differentialgleichungen erster Ordnung," Springer Books, in: Eine Einführung in gewöhnliche Differentialgleichungen, chapter 0, pages 11-43, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-3996-3_2
    DOI: 10.1007/978-81-322-3996-3_2
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