Lineare Algebra Für Die Natur- Und Ingenieurwissenschaften: Vektoren, Matrizen Und Lineare Gleichungssysteme
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Dieses Lehrbuch behandelt die zentralen Themen der Linearen Algebra einschlie lich ihrer Anwendungen.
Neben einer systematischen Einf�hrung der Rechenoperationen mit Vektoren und Matrizen werden entsprechende Rechengesetze angegeben, und es wird erkl�rt, warum diese gelten. Zahlreiche sehr ausf�hrlich vorgerechnete Beispiele machen das Lehrbuch zu einer wertvollen Basis f�r das Selbststudium oder zur Vorbereitung auf Pr�fungen. Viele dieser Beispiele geben au erdem einen Einblick, welche Problemstellungen mittels der Vektor- und Matrizenrechnung behandelt werden k�nnen.
Neben allgemeinen L�sungsstrategien f�r lineare Gleichungssysteme werden L�sungsalgorithmen diskutiert, welche auf spezifische Anwendungsgebiete abgestimmt sind - z. B. Algorithmen zur L�sung von tridiagonalen Gleichungssystemen, von Gleichungssystemen mit einer symmetrischen, positiv definiten Matrix und von Gleichungssystemen, die in der Ausgleichungsrechnung auftreten.F�r eine ganze Reihevon Problemen wie der L�sung linearer Gleichungssysteme, der Berechnung von Determinanten und der Berechnung der Inversen einer Matrix werden verschiedene Algorithmen vorgestellt. Bei der Nutzung dieser unterschiedlichen Algorithmen zeigt sich, dass manche davon eine sehr hohe Rechenzeit erfordern, w�hrend man mit anderen das Rechenergebnis schon nach einer sehr geringen Rechenzeit erh�lt. Um einsch�tzen zu k�nnen, welche der Algorithmen wann bevorzugt eingesetzt werden sollten, wird f�r viele Algorithmen eine Analyse des Aufwandes an Rechenoperationen durchgef�hrt.
Der Inhalt
Vektoren - Matrizen - Rechnen mit Vektoren und Matrizen - allgemeine L�sungsalgorithmen f�r lineare Gleichungssysteme - L�sungsalgorithmen f�r spezielle Gleichungssysteme
Die Zielgruppen
Studierende der Natur- und Ingenieurwissenschaften
Prof. Dr. Michael Jung lehrt seit 2004 Mathematik und deren fachspezifischen Anwendungen in Studiengängen der Fakultäten Geoinformation und Informatik/Mathematik der Hochschule für Technik und Wirtschaft Dresden.
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