微积分与分析导论
Introduction to calculus and analysis
Richard Courant、Fritz John · 初版 1965 年
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摘自前言：(...) 本书面向各层次的学生、数学家、科学家和工程师。它并不试图通过粉饰难点来让这门学科显得容易，而是试图通过阐明整体的内在联系与目的来帮助真正感兴趣的读者。我们有时将关于基础性质的冗长讨论延后至各章附录中，以免阻碍读者接触丰富的知识内容。各章末尾提供了大量的例题与习题。有些颇具挑战性
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怎么会没人提 Courant 和 John 写的《Introduction to Calculus and Analysis》（微积分和数学分析引论）呢？我都快看哭了。
How can nobody here mention Courant and John's Introduction to Calculus and Analysis? I think I'm going to cry.
Richard Courant 和 Fritz John 写的《Introduction to Calculus and Analysis》。这本书把微积分中许多概念的直观引出实例讲得非常透彻，这对我这个初学者来说至关重要。太多次我读数学……
Introduction to Calculus and Analysis, by Richard Courant and Fritz John. This book clearly explained many of the motivating examples of the concepts in Calculus, which was important to me as a beginning student. Too many times I read math…
……深刻的洞见和理解，你才能去创新和推进。令人惊讶的是，竟然有那么多博士从未真正精通他们所在的领域。但这确实很难，也特别耗费时间。我心中理想的数学教材是 Richard Courant 的《Introduction to calculus and analysis》。它完美融合了数学严谨性与深刻的直觉。可惜我当年的微积分入门教材不是它。它曾经是西方标准的入门教材。我……
…insights and understanding can you innovate and advance. It is remarkable how many Ph.D.'s never master their fields. But it is hard and time consuming. My ideal of math textbook is Richard Courant's "Introduction to calculus and analysis." It is a perfect blend of mathematical rigor and insightful intuition. It is sad that I didn't have it as my introductory calculus textbook. It used to be the standard intro textbook in the West. I…
在众多教材中，我几乎唯一真正喜欢并从中获益的是 Courant 的《Differential and Integral Calculus》以及更新版《Introduction to Calculus and Analysis》。它并没有采用现代常见的主题划分方式，而是在两卷中把单变量微积分、多变量微积分和实分析连贯地作为一整套长脉络来处理，但是其文笔……
Among the many texts almost the only one I really liked and learnt from is Courant's "Differential and Integral calculus" and the newer edition "Introduction to Calculus and Analysis". It doesn't do the typical modern division of topics and instead treats single-variable calculus, multi-variable calculus and real analysis in its two volumes in a single long sequence, but the writing…
……这毫无疑问是你所能采取的最棒、收益最高的行动。这些书里的任何一本都能改变你的人生。1. Spivak《Calculus》 2. Apostol《Calculus》第 I 和 II 卷 3. Courant 和 John 的《Introduction to Calculus and Analysis》第 I、IIA 和 IIB 卷。对于要求没那么苛刻的计算机科学或物理专业学生，我会推荐选第 3 种，它最像费曼物理学讲义的风格。另外两本书的严谨性它全都有，但讲解方式更……
…this is unquestionably the single best, most profitable action you can take. Any one of these books can change your life. 1. Spivak Calculus 2. Apostol Calculus vol. I and II 3. Courant and Johns, Introduction to Calculus and Analysis vol. I, IIA and IIB For the more casual computer science or physics major, I'd go with choice 3 which resembles the Feynmann lectures the most. All the rigour of the other two is there but in a more…
……补码运算）。至于抽象作为现代数学中那些看似人为制造的难点的根源，正如 Courant 的《Differential and Integral Calculus》（即《Introduction to Calculus and Analysis》第一版）[2]的引言所言：“将分析学呈现为一个不涉及其起源和目的的封闭真理体系，诚然具有美学上的魅力，并满足了深刻的哲学需求。但这种态度……”
…complement arithmetic). As for abstraction as a source of seemingly artificial difficulty in modern mathematics, from the introduction to Courant's Differential and Integral Calculus, the first edition of Introduction to Calculus and Analysis[2], The presentation of analysis as a closed system of truths without reference to their origin and purpose has, it is true, an aesthetic charm and satisfies a deep philosophical need. But the attitude…