Introduction to calculus and analysis
by Richard Courant, Fritz John · first published 1965
83% recommend17% neutral
Why HN recommends it
A rigorous yet motivated treatment of calculus and analysis that integrates single-variable, multivariable, and real analysis, with clear motivating examples. Suited to beginners and readers seeking deep understanding.
Summarised by Claude from recommending comments
From the Preface: (...) The book is addressed to students on various levels, to mathematicians, scientists, engineers. It does not pretend to make the subject easy by glossing over difficulties, but rather tries to help the genuinely interested reader by throwing light on the interconnections and purposes of the whole. Instead of obstructing the access to the wealth of facts by lengthy discussions of a fundamental nature we have sometimes postponed such discussions to appendices in the various chapters. Numerous examples and problems are given at the end of various chapters. Some are challengi
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How can nobody here mention Courant and John's Introduction to Calculus and Analysis? I think I'm going to cry.
on “Ask HN: Learning advanced math” ↗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…
on “Ask HN: The book that did it for you in math and/or CS?” ↗…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…
on “Why I’m taking full responsibility for my education” ↗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…
on “Math topics useful for computer science/programming” ↗…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…
on “Ask HN: Are there books for mathematics like Feynman's lectures on physics?” ↗…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…
on “When did computer science theory get so hard?” ↗…first rank operated ... sometimes even with mystical associations as in references to 'infinitesimals' or 'infinitely small quantities.'" I believe we now use the "epislon delta" definition of limits. "Introduction to Calculus and Analysis" Volume 1
on “When did computer science theory get so hard?” ↗