数学家、计算机科学家和物理学家用的微积分 [pdf]
Calculus for Mathematicians, Computer Scientists, and Physicists [pdf]

原始链接: https://mathcs.holycross.edu/~ahwang/print/calc.pdf

该文档似乎是一本关于微积分和实分析基础概念的综合教科书或课程大纲。它从“数学语言”和“数学本质”开始,然后深入研究集合论、逻辑以及各种数系——自然数、整数、有理数、实数和复数。 文档的大部分篇幅都致力于函数,探讨基本定义、分类、复合以及线性算子。文本的核心是微积分,涵盖极限、连续性、数列、级数、微分和积分——包括瑕积分和基本定理。 除了基础微积分,它还扩展到更高级的主题,如函数序列、幂级数以及使用泰勒级数进行近似。该文本还包括关于初等函数(对数、指数、三角函数)的部分,以及对复分析的简要介绍。最后,它涉及数值和函数逼近技术。文档以参考文献和索引结尾。

一本名为《为数学家、计算机科学家和物理学家准备的微积分》的 PDF 教材正在 Hacker News 上讨论。讨论的核心在于编写一本既能满足高级学生严格要求,又不至于成为完整的实分析教材的微积分书籍的难度。 一位评论员指出,这本书似乎通过专注于基础词汇和与线性代数的联系,而不是陷入过于复杂的收敛性证明,成功地应对了这一挑战。用户也在询问这本书的可访问性——需要什么水平的数学背景——以及是否有实体书,因为目前似乎只有 PDF 版本。 广泛的目标读者(数学家、计算机科学家和物理学家)也引发了关于这本书是否能为这三个群体达到适当的难度水平的讨论。
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