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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.
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.
"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.