Analysis II für Physiker by Wulf-Dieter Geyer PDF

By Wulf-Dieter Geyer

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8 .. . ... ... . ... .. .. . . . .. .. .. .. .. .. .. ... .. ... .. . .. .. 1 y =f (x) y =f (x) 0 0 1 28 . ... .... .. .... .. ... .. . . .. . . .. . . .. . . .. . . . .. . . .. . .. .. 16 . . .. .. . .. .. .. . .. . . .. .. .. . .. .. . .. .. .. . .. . . .. . 0 0 1 37. Die Folge (Pi (t)) der rekursiv durch P = 0 ; Pi (t) = Pi (t) + 21 (t Pi (t)) 1 (2) 2 +1 de niertenpPolynome Pi konvergiert auf dem Intervall 0; 1] monoton und gleichma ig gegen die Funktion t .

4. Wendet man auf den Weg aus Beispiel 3 die lineare Transformation x 7! ax y by (x; y 2 IR) mit a > b > 0, also eine Streckung in beiden Achsenrichtungen mit verschiedenen Dehnungsfaktoren, an, so entsteht aus dem Kreis eine Ellipse 0; 2 ] 3 t 7! (a cos t; b sin t) ; deren Spur durch die Gleichung x + y a b 2 ................................................................. ..............

B p E a; a; . E ; b .. .. .. .. Die Bahnkurven des Keplerschen 2-Korperproblems in der Newtonschen Mechanik sind nicht nur Ellipsen, sondern auch Hyperbelaste und Parabeln. So gibt es manche Kometen, die die Sonne periodisch auf Ellipsen "umkreisen\, andere haben Hyperbelbahnen und kommen nur einmal in die Nahe des Sonnensystems. Auch die Hyperbel ist punktsymmetrisch zum Mittelpunkt (0; 0).

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Analysis II für Physiker by Wulf-Dieter Geyer


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