分析方法（修訂版）

《分析方法（修訂版）》是2018年世界圖書出版公司出版的著作，作者是[美] R.S.斯特里查茲（Robert S.Strichartz）。

基本介紹

• 中文名：《分析方法（修訂版）》
• 作者：[美]R.S.斯特里查茲（Robert S.Strichartz）
• 出版時間：2018年10月01日
• 出版社：世界圖書出版公司

內容簡介

Mathematics is more than a collection of theorems， definitions，

problems and techniques； it is a way of thought. The same can be said

about an individual branch of mathematics， such as analysis. Analysishas its roots in the work of Archimedes and other ancient Greek ge-ometers， who developed techniques to find areas， volumes， centers of

gravity， arc lengths， and tangents to curves. In the seventeenth centurythese techniques were further developed， culminating in the inventionof the calculus of Newton and Leibniz， During the eighteenth centu-ry the calculus was fashioned into a tool of bold computational powerand applied to diverse problems of practical and theoretical interest.At the same time the foundation of analysis-the logical justificationfor the success of the methods-was left in limbo. This had practicalconsequences： for example， Euler-the leading mathematician of theeighteenth century-developed all the techniques needed for the studyof Fourier series， but he never carried out the project. On the contrary，he argued in print again，st the possibility of representing functions asFourier series， when this proposal was put forth by Daniel Bernoulli，and his argument was based on fundamental misconceptions concerningthe nature of functions and infinite series.

In the nineteenth century， the problem of the foundation of anal-ysis was faced squarely and resolved. The theory that was developedforms most of the content of this book. We will describe it in its logical order， starting from the most basic concepts such as sets and numbers and building up to the more involved concepts of limits， continuity，derivative， and integral， The actual historical order of discovery was almost the reverse； much like peeling a cabbage， mathematicians be-gan with the outermost layers and worked their way inward. Cauchy and Bolzano began the process in the 1820s by developing the theo-ry of functions without defining the real numbers. The first rigorous definition of the real number system came in the work of Dedekind，Weierstrass， and Heine in the 1860s. Set theory came later in the work of Cantor， Peano， and Frege.

The consequences of the nineteenth century foundational work were enormous and are still being felt today. Perhaps the least important consequence was the establishment of a logically valid explanation of the calculus. More important， with the clearing away of the concep-tual murk， new problems emerged with clarity and were developed into important theories. We will give some illustrations of these new nineteenth century discoveries in our discussions of differential equa-tions， Fourier series， higher dimensional calculus， and manifolds. Most important of all， however， the nineteenth century foundational work paved the way for the work of the twentieth century. Analysis today is a subject of vast scope and beauty， ranging from the abstract to the concrete， characterized both by the bold computational power of the eighteenth century and the logical subtlety of the nineteenth century.Most of these developments are beyond the scope of this book or at best merely hinted at. Still， it is my hope that the reader， after hav-ing entered so deeply along the way of analysis， will be encouraged to continue the study.

作者簡介

本書作者Robert S. Strichartz（R.S.斯特里查茲）是美國康奈爾大學教授，該校是一所世界私立研究型大學，是著名的常春藤聯盟成員。