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Mathematik 2 für MEB/MM
(2018)
Vektorrechnung: Darstellung von Vektoren, Komponenten, Einheitsvektor, Addition, Subtraktion, Projektion, Skalarprodukt, Kreuzprodukt, Geraden, Ebenen Lineare Algebra: Darstellung, Rechnen mit Matrizen und Vektoren, Drehmatrix, lineare Gleichungssysteme (Eliminationsverfahren GAUSS oder GAUSS-JORDAN, inverse Matrix, über- und unterbestimmte Systeme), Determinanten (Rang einer Matrix, SARRUSsche Regel, CRAMERsche Regel), Eigenwerte und Eigenvektoren einer quadratischen Matrix
Fourier-Reihen: (Fourier-Reihe, reell, komplex, beliebige Periode, punktweise Funktion), Wellen (zeitliche und räumliche Ausbreitung von Wellen, Amplitude, Frequenz, Phase)
Differentialrechnung für Funktionen von mehreren Variablen: graphische Darstellung, skalare und Vektorfelder, partielle Ableitung, Differenzial, Gradient, Kettenregeln, Fehlerfortpflanzung
Integralrechnung für Funktionen von mehreren Variablen: konstante Grenzen, Produktzerlegung, Koordinatensysteme, Polarkoordinaten, Zylinderkoordinaten, Kugelkoordinaten, Trägheitsmomente, variable Grenzen
Gewöhnliche Differentialgleichungen: Klassifikation, Anfangswerte bzw. Randbedingungen, Trennung der Veränderlichen, Variation der Konstanten, DGL mit konstanten Koeffizienten, e-Ansatz, homogene, inhomogene DGL, charakteristische Gleichung, inhomogener Lösungen, Systeme linearer DGL Laplace-Transformation: Eigenschaften, Lösung einer DGL, Korrespondenztabellen, Partialbruchzerlegung, Rücktransformation, Übertragungsfunktion
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