数学分析
Mathematical Analysis
Tom M. Apostol · 初版 1957 年
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本书提供了从初等微积分到实变函数与复变函数论高级课程的过渡，并引导读者领略贯穿于现代分析学中的若干抽象思维。
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Mathematical Analysis
Tom M. Apostol · 初版 1957 年
本书提供了从初等微积分到实变函数与复变函数论高级课程的过渡，并引导读者领略贯穿于现代分析学中的若干抽象思维。
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Walter Rudin 关于实分析的那本书通常被视为该领域的经典。不过，你也可以看看 Tom M. Apostol 的《Mathematical Analysis》，它有助于培养对这门学科良好的直觉。
Walter Rudin's book on Real Analysis is normally considered as classic in this area. However, you can also take a look at Mathematical Analysis by Tom M. Apostol, which helps in developing good intuition about the subject.
……线性代数系统} 或许可以抽个晚上看看 LINPACK 的文档。某个周末找点乐子，快速翻一遍 Tom M. Apostol《数学分析：高等微积分的现代方法》（Mathematical Analysis: A Modern Approach to Advanced Calculus）里高斯……斯托克斯定理那几部分，不用太把证明当回事，主要是看看物理科学和工程学是怎么看待多元微积分的。Neveu 是一本很棒的终极概率论……
…Linear Algebraic Systems,\/} Maybe spend an evening on the documentation of LINPACK. Some weekend of great fun, take a fast pass through the Gauss, ..., Stokes theorem parts of Tom M.\ Apostol, {\it Mathematical Analysis: A Modern Approach to Advanced Calculus,\/} where don't take the proofs very seriously but to see how physical science and engineering look at calculus of several variables. Neveu is a great last probability…
我的建议是先读 Tom M. Apostol 的《单变量微积分与线性代数导论》（One-Variable-Calculus with and introduction to Linear Algebra），然后读《数学分析》（Mathematical Analysis）。这两本书搭配起来简直绝配！
My recommendation is "One-Variable-Calculus with and introduction to Linear Algebra" by Tom M. Apostol, followed by "Mathematical Analysis". Both books form a great combination!
……在 Google 上搜想在 YouTube 上找份拷贝，但什么也没找到。有人知道那场讲座在哪吗？我最喜欢的书之一，绝版很久之后我特地费劲淘了本二手，就是 Tom M. Apostol 的《数学分析：高等微积分的现代方法》（Mathematical Analysis: A Modern Approach to Advanced Calculus，Addison-Wesley，马萨诸塞州雷丁，1957年）。那里的高等微积分更贴近你本科物理教授看它的视角。在学 Rudin、外代数……的时候手头有一本太棒了
…a Google search looking for a copy on YouTube and found nothing. Anyone know where that lecture is? One of my favorite books, I worked to buy used long after it was out of print, is Tom M. Apostol, Mathematical Analysis: A Modern Approach to Advanced Calculus, Addison-Wesley, Reading, Massachusetts, 1957. And that is advanced calculus more like your ugrad physics prof will see it. Great to have when studying Rudin, exterior…
Apostol 的微积分教材是我第一次接触“真正”基于证明的数学，而且我实分析也是看他的《数学分析》（Mathematical Analysis）学的。美好的时光啊；他的书教会了我很多。他写得清晰简练；读 Apostol 的书时，总觉得没有一个字是多余的。我强烈建议去读读他的……
Apostol's calculus texts were my first experience with 'real' proof-based mathematics, and I also learned real analysis through his Mathematical Analysis book. Good times; his books taught me a lot. He wrote with clarity and conciseness; when I read Apostol it always seemed like not a single word was added unnecessarily. I highly suggest picking up his…
……比如 Spivak、Apostol、Rudin 这些经典。Rudin 的《实分析与复分析》（Real and Complex Analysis），以及 Spivak 和 Apostol 各自同名为《微积分》（Calculus）的两本书。还有 Apostol 那本更简练且影响深远的《数学分析》（Mathematical Analysis）。另外 Spivak 的那本神作小册子《流形上的微积分》（Calculus On Manifolds）对我触动很大。除了这些比较“经典的数学”书之外，我还想提两本让我大开眼界、整体极其惊艳的非主流书：……
…with classics like Spivak, Apostol, Rudin. "Real and Complex Analysis" by Rudin, and the two books both named "Calculus" from Spivak and Apostol. But also from Apostol his more concise and far-reaching "Mathematical Analysis". And from Spivak his small gem "Calculus On Manifolds" made quite a dent on me. Other than more "classic math" books, I also wanted to mention two outliers that I found eye-opening and generally awesome:…