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Home > Mathematics and Science Textbooks > Mathematics > Calculus and mathematical analysis > Angewandte Analysis in einer Unbekannten: (Springer-Lehrbuch)
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Angewandte Analysis in einer Unbekannten: (Springer-Lehrbuch)

Angewandte Analysis in einer Unbekannten: (Springer-Lehrbuch)


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About the Book

Dieses Buch gibt auf eine sehr umfassende und unmissverständliche Art und Weise die "praktische" Analysis in einer Veränderlichen wider. Es unterscheidet sich erheblich von klassischen Textbüchern im europäischen Raum, die meistens abstrakte Analysis voranstellen, die dann durch Beispiele illustriert wird. Im vorliegenden Buch wird die umgekehrte Richtung praktiziert, von konkreten Aufgaben eine adequate Analysis herzuleiten. Dieser Zugang liegt im Trend der Zeit und erfährt großen Zuspruch, auch und besonders in Vorlesungen für Nichtmathematiker. Ein weiteres Merkmal ist die hervorragende Didaktik: Im Gegensatz zu vergleichbaren deutschsprachigen Lehrbüchern hat dieses einen erfrischenden, wirklich bemerkenswerten Aufbau und einen gewissen Unterhaltungswert. Es ist sehr motivierend und dadurch angenehm zu lesen.

Table of Contents:
Einführung.- Zahlen und Funktionen, Folgen und Grenzwerte.- Mathematische Modellierungen.- Natürliche Zahlen sind einfach nicht genug.- Die Unendlichkeit und die vollständige Induktion.- Rationale Zahlen.- Funktionen.- Polynome.- Funktionen, Funktionen und noch mehr Funktionen.- Lipschitz-Stetigkeit.- Folgen und Grenzwerte.- Wir lösen das Modell vom matschigen Hof.- Reele Zahlen.- Funktionen reeller Zahlen.- Der Bisektionsalgorithmus.- Inverse Funktionen.- Fixpunkte und kontrahierende Abbildungen.- Differenzial- und Integralrechnung.- Die Linearisierung einer Funktion in einem Punkt.- Wir analysieren das Verhalten eines Populations-Modells.- Interpretationen der Ableitung.- Differenzierbarkeit auf Intervallen.- Nützliche Eigenschaften der Ableitung.- Der Mittelwertsatz.- Ableitungen von inversen Funktionen.- Modellierung mit Differenzialgleichungen.- Unbestimmte Integration.- Integration.- Eigenschaften des Integrals.- Anwendungsmöglichkeiten des Integrals.- Raketenantriebe und der Logarithmus.- Die konstante relative Änderungsrate und die Exponentialfunktion.- Ein Masse-Feder-System und die trigonometrischen Funktionen.- Die Fixpunktiteration und das Newton-Verfahren.- Sie möchten Analysis? Hier ist sie.- Definitionen der Stetigkeit und der Differenzierbarkeit.- Folgen von Funktionen.- Erleichterte Integration.- Heikle Grenzwerte und hässliches Verhalten.- Der Approximationssatz von Weierstraß.- Das Taylor-Polynom.- Polynominterpolation.- Nichtlineare Differenzialgleichungen.- Die Picard-Iteration.- Das explizite Euler-Verfahren.

Review :
From the reviews of the English edition: Traditional applied mathematicians and numerical analysts have always expressed their frustration about the abstract approach to the teaching of real analysis, which does not serve the needs of students. This frustration has culminated in the writing of this book in which Estep combines the basic ideas of real analysis and numerical analysis in an applied framework. This framework is beautifully presented in the context of a fundamental approach to applied mathematical problem solving, which is to approximate the solution of a physical model. The book is written in an engaging manner, beginning with less-difficult concepts and successively progressing through several degrees of increasing difficulty. It is not written in a theorem-proof style quite reminiscent of rigorous analysis textbooks. Background and review material and numerous examples, including visualizations and alternate explanations of some key ideas, are provided in a very appealing manner. Abstract concepts are carefully explained and supported with a wealth of examples and illustrations and a wonderful collection of problems, a few elementary enough for any beginner. SUMMING UP: Highly recommended. Upperdivision undergraduates through professionals. SCIENCE AND TECHNOLOGY MATHEMATICS July 2003, D.E. Bentil.


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Product Details
  • ISBN-13: 9783540218982
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Height: 235 mm
  • No of Pages: 678
  • Returnable: Y
  • Width: 155 mm
  • ISBN-10: 354021898X
  • Publisher Date: 08 Sep 2004
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Series Title: Springer-Lehrbuch


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Angewandte Analysis in einer Unbekannten: (Springer-Lehrbuch)
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