Intermediate Real Analysis
Intermediate Real Analysis
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中级实分析
DOI：
10.2307/3616367
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发表时间：
1982
期刊：
影响因子：
--
通讯作者：
E. Fischer
中科院分区：
文献类型：
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作者：
E. Fischer
如今有大量关于分析入门的书籍出版，其中许多是由一流数学家撰写的。因此，另一本此类书的出版值得辩护。我教授分析多年，期间使用过各种文本。这些书在数学方面质量很好，但不能满足我所教学生的需求。它们是为数学家而写的，而不是为那些首先渴望获得数学地位的人而写的。填补这一空白的愿望催生了本书的写作。本书旨在作为分析入门课程的教材。它的读者很可能是正在接受本科教育最后一个季度的数学、科学或工程专业的学生。第一门分析课程的目的是为学生提供坚实的分析基础，让他熟悉高等数学中使用的仔细思维，并为他提供进一步研究的工具。我们所接触的典型学生已经完成了三个学期的微积分课程，可能还完成了微分方程的入门课程。他甚至可能接触过一两个学期的现代代数。一直以来，他的训练很可能都是凭直觉，用启发法代替了证明。这可能适合他那个发展阶段。
There are a great deal of books on introductory analysis in print today, many written by mathematicians of the first rank. The publication of another such book therefore warrants a defense. I have taught analysis for many years and have used a variety of texts during this time. These books were of excellent quality mathematically but did not satisfy the needs of the students I was teaching. They were written for mathematicians but not for those who were first aspiring to attain that status. The desire to fill this gap gave rise to the writing of this book. This book is intended to serve as a text for an introductory course in analysis. Its readers will most likely be mathematics, science, or engineering majors undertaking the last quarter of their undergraduate education. The aim of a first course in analysis is to provide the student with a sound foundation for analysis, to familiarize him with the kind of careful thinking used in advanced mathematics, and to provide him with tools for further work in it. The typical student we are dealing with has completed a three-semester calculus course and possibly an introductory course in differential equations. He may even have been exposed to a semester or two of modern algebra. All this time his training has most likely been intuitive with heuristics taking the place of proof. This may have been appropriate for that stage of his development.