Applied Analysis - J.K. Hunter, B. Nachtergaele

Название: Applied Analysis
Автор: J.K. Hunter, B. Nachtergaele
Категория: Математика
Тип: Книга
Дата: 30.12.2008 15:56:56
Скачано: 82
Описание: Mathematical knowledge and sophistication, computational power, and areas of application are expanding at an enormous rate. As a result, the demands on the training of applied mathematicians are increasing all the time. It is therefore not easy to decide what should constitute the core mathematical training of an applied mathematician. We take the view that every applied mathematician, whatever his or her ultimate area of interest may turn out to be, should have a grounding in the fundamentals of analysis. The aim of this book is to supply an introduction for beginning graduate students to those parts of analysis that are most useful in applications. The material is selected for its use in applied problems, and is presented as clearly and simply as we are able, but without the sacrifice of mathematical rigor. We focus on ideas of central importance, and attempt to avoid technicalities and detours into areas of more specialized interest. While we make every effort to motivate the ideas introduced, and include a variety of examples from different fields, this book is first and foremost about analysis. We do not assume extensive mathematical prerequisites of the reader. The book is intended to be accessible to students from a wide variety of backgrounds, including undergraduate students entering applied mathematics from non-mathematical fields, and graduate students in the sciences and engineering who would like to learn analysis. A basic background in calculus, linear algebra, ordinary differential equations, and some familiarity with functions and sets should be sufficient. We occasionally use some elementary results from complex analysis, but we do not develop any methods from complex analysis in the text. We provide detailed proofs for the main topics. We make no attempt to state results is maximum generality, and instead illustrate the main ideas in simple, concrete settings. We often return to the same ideas in different contexts, even if this leads to some repetition of previous definitions and results. We make extensive use of examples and exercises to illustrate the concepts introduced. The exercises are at various levels; some are elementary, although we have omitted many of the routine exercises that we assign while teaching the class, and some are harder and are an
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