Welcome to real analysis : continuity and calculus, distance and dynamics
著者
書誌事項
Welcome to real analysis : continuity and calculus, distance and dynamics
（AMS/MAA textbooks, v. 70）
MAA Press ; an imprint of the American Mathematical Society, c2022
- : pbk.
大学図書館所蔵 件 / 全1件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references (p. 355) and index
内容説明・目次
内容説明
Welcome to Real Analysis is designed for use in an introductory undergraduate course in real analysis. Much of the development is in the setting of the general metric space. The book makes substantial use not only of the real line and $n$-dimensional Euclidean space, but also sequence and function spaces. Proving and extending results from single-variable calculus provides motivation throughout. The more abstract ideas come to life in meaningful and accessible applications. For example, the contraction mapping principle is used to prove an existence and uniqueness theorem for solutions of ordinary differential equations and the existence of certain fractals; the continuity of the integration operator on the space of continuous functions on a compact interval paves the way for some results about power series.
The exposition is exceedingly clear and well-motivated. There are a wide variety of exercises and many pedagogical innovations. For example, each chapter includes Reading Questions so that students can check their understanding. In addition to the standard material in a first real analysis course, the book contains two concluding chapters on dynamical systems and fractals as an illustration of the power of the theory developed.
目次
Where we're starting and where we're going
Essential tools
Metric spaces
Sequences
Continuity
Compactness and connectedness
The derivative
The Riemannn integral
Sequences of functions
Chaos in discrete dynamical systems
The Hausdorff metric and fractals
Bibliography
Index
「Nielsen BookData」 より