Download e-book for iPad: Applied & Computational Complex Analysis by Peter Henrici

By Peter Henrici

Provides functions in addition to the fundamental thought of analytic capabilities of 1 or numerous complicated variables. the 1st quantity discusses functions and simple conception of conformal mapping and the answer of algebraic and transcendental equations. quantity covers issues commonly hooked up with traditional differental equations: specified features, essential transforms, asymptotics and persevered fractions. quantity 3 info discrete fourier research, cauchy integrals, building of conformal maps, univalent capabilities, capability concept within the airplane and polynomial expansions.

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3: Schaltalgebra Erkl¨ aren Sie folgende Begriffe: Schaltvariable, Dualit¨atsprinzip, Logikgesetze, Logikfunktion, bin¨ are Logikfunktion, NOR-Funktion, NAND-Funktion, Minterm, Maxterm, disjunktive bzw. konjunktive Normalform. ¨ 1. Richtig oder falsch? ) a) a·0 = 1 b) a+a = 1 c) a·a = 0 d) a · b = a·b e) a · b = a+b 26 1 Logik und Mengen 2. Bilden Sie mithilfe des Dualit¨ atsprinzips aus folgenden g¨ ultigen Regeln weitere g¨ ultige Regeln: a) a · 1 = a b) a · (b + c) = (a · b) + (a · c) c) a · (a + b) = a 3.

3, −2, −1, 0, 1, 2, 3, . } heißt Menge der ganzen Zahlen. Jede nat¨ urliche Zahl ist auch eine ganze Zahl: N ⊆ Z. Die ganzen Zahlen sind wie die nat¨ urlichen Zahlen geordnet, k¨ onnen also ebenso auf einer Kette aufgereiht werden. Beachten Sie dabei, dass m < n ⇔ −n < −m. Beispiel: Es ist 1 < 2, jedoch −2 < −1 (und nicht −1 < −2)! Die rationalen Zahlen Q Auch wenn uns nun bereits alle ganzen Zahlen zur Verf¨ ugung stehen, so stoßen wir doch sehr bald wieder auf Probleme: Es gibt z. B. keine ganze Zahl x, die die Gleichung 3x = 2 erf¨ ullt.

D) In der Nacht ist keine Katze grau. 5. Gilt ⇒ oder sogar ⇔? Setzen Sie ein und formulieren Sie sprachlich: a) x durch 4 teilbar . . x durch 2 teilbar. b) x gerade Zahl . . x + 1 ungerade Zahl. c) Auf einem Schild steht: Dienstag ist Ruhetag“. Wie verstehen Sie das? Diens” tag . . Ruhetag. 6. “ F¨ ur mich gilt: ” ” a ⇒ b, also Wenn ich die Pr¨ ufung bestehe, dann feiere ich“. Was l¨asst sich ” daraus u ufung nicht bestehe? 6 Ubungen 29 7. Geben Sie die Menge in beschreibender Form an: a) A = {4, 5, 6} b) B = {−1, 0, 1} c) C = {.

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