Courant & John's Introduction to Calculus and Analysis

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Discussion Overview

The discussion centers around Courant & John's "Introduction to Calculus and Analysis, Volume II," specifically regarding its structure, content, and the experiences of participants with the text. The conversation touches on the number of chapters, the distinction between different editions, and the perceived rigor and depth of the material.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about the number of chapters in Volume II, noting a 4-chapter reprint.
  • Another participant clarifies that there are two parts to the second volume, with the reprint being the first part.
  • Some participants mention that the newer editions from Springer consist of three volumes, while earlier editions had only two volumes.
  • A participant expresses satisfaction with the first volume, describing it as an excellent text and expressing interest in the second volume.
  • There are repeated claims that reading both volumes would provide a comprehensive understanding of calculus.
  • One participant reflects on their experience with Stewart's book and considers Courant's work for a more rigorous approach.
  • Another participant praises Courant's teaching style, highlighting the intuitive nature of the proofs and the quality of exercises, while noting a preference for the "Courant & John" version over the original "Courant" edition.
  • A participant seeks clarification on what is meant by the "vanilla" version of Courant's work.
  • Clarification is provided that "vanilla" refers to the volumes titled "Differential & Integral Calculus."

Areas of Agreement / Disagreement

Participants express a range of opinions about the merits of Courant's texts, with some praising its rigor and depth while others compare it to different calculus resources. There is no consensus on the best edition or the overall preference between different versions of Courant's work.

Contextual Notes

Some participants express uncertainty about the specific structure of the volumes and the differences between editions, indicating a need for further clarification on these points.

devious_
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Does anyone know how many chapters Courant & John's "Introduction to Calculus and Analysis, Volume II" has? Because I've found a 4 chapter reprint, and was wondering if I should get it.
 
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Nevermind... I think I understand now: there are two parts to the second volume, and this happens to be the first one.
 
the new ones of springer are of total of 3 volumes (including the first volume), while the first editions are only 2 books.
but quite hefty, and with applications to physics.
 
Indeed. I saw the second volume at my school's library the other day. It was huge. :smile:

I own the first volume and, having read through large chunks of it, find it an excellent text. So I decided to see if the same applies to the second volume.
 
if you read those 2 volumes, no one will know more calculus than you.
 
mathwonk said:
if you read those 2 volumes, no one will know more calculus than you.


Wow, Mathwonk seems to be really pleased with Courant. So much so that I'm contemplating picking up the two volumes. I've found Stewart's book to be a breeze for the most part(self-teaching). Perhaps I should look into something more detailed and rigorous?

What is it about Courant's book that impresses you most, if you don't mind my asking? Is it the rigor? The depth? I'd be really interested in knowing.
 
mathwonk said:
if you read those 2 volumes, no one will know more calculus than you.

Not even Richard Courant.
 
duke_nemmerle said:
What is it about Courant's book that impresses you most, if you don't mind my asking? Is it the rigor? The depth? I'd be really interested in knowing.
Courant is amazing. I promise you that you can find anything related to calculus (be it application or theory) in that text.

I just simply love his approach. He doesn't use the usually dry definition-theorem-corollary approach, but instead he actually motivates everything and gives proofs that feel so intuitive you can't help but feel they're actually informal. Sometimes the more technical proofs (along with other interesting examples, applications, etc.) are left in the appendices so as to not hinder your first attempt at understanding the material. Plus the exercises are just fantastic! You can find a lot of difficult problems in there (even ones that appear in Spivak).

I actually picked up the first volume after mathwonk recommended it. At first I didn't like it all that much, but now it's grown on me. Personally I recommend the "Courant & John" version as opposed to the vanilla "Courant" one. I don't know why, but I liked the structure of the former more.
 
devious, when you mean vanilla one, do you refer to the volumes entitled:"differential & integral calculus"?
 
  • #10
Yes, those. I read "Introduction to Calculus and Analysis".
 

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