Introduction to Calculus and Analysis

Click For Summary

Discussion Overview

The discussion revolves around the books by Richard Courant and Fritz John, specifically focusing on their content, rigor, and differences compared to the original Courant text. Participants share their experiences and seek advice regarding the use of these texts in the context of learning calculus and analysis.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants express that Courant's book is highly regarded for its quality and rigor, suggesting it may be challenging but rewarding.
  • One participant mentions using "Differential and Integral Calculus" by Courant and finds it to be very good.
  • Another participant notes that they had to read sections multiple times to fully understand the material, indicating the text's complexity.
  • It is suggested that the Courant and John text is a rewrite of the original, incorporating more rigorous methods from the mid-20th century, but some prefer the original for its intuitive approach.
  • A participant requests clarification on the specific differences between the two texts and examples to illustrate these differences.
  • It is mentioned that the Courant and John text focuses more on analysis, while the original provides a full exposition on calculus.
  • One participant expresses confusion about the relationship between mathematical analysis and calculus, questioning whether they are the same subject.

Areas of Agreement / Disagreement

Participants express differing opinions on the merits of the original Courant text versus the Courant and John rewrite, indicating a lack of consensus on which is preferable. There is also uncertainty regarding the relationship between calculus and mathematical analysis.

Contextual Notes

Some discussions highlight the subjective nature of preferences for the original versus the rewritten text, and there are unresolved questions about specific differences and definitions related to calculus and analysis.

WORLD-HEN
Messages
45
Reaction score
0
Has anyone used this set of books by Richard Courant and Fritz John? If so, I would like some advice about them.
 
Physics news on Phys.org
From what I know, Courant's book is close to the very top; in quality and rigour.
This might make it a tough going, but if you persevere, you will be amply rewarded.
 
Iuse Differential and Integral Calculus y Couranr. It' really good
 
Yes, I've noticed, I had to read a few sections 2-3 times before I understood everything. But since you say its one of the best, I am going to continue with it, thanks.
 
courant and john is a rewrite of courant, attempting to incorporate some more rigorous and precise methods of the mid 20th century. it is a wonderful book, but i prefer the original courant as more intuitive and less stuffy.

i have learned and taught from both and they are not all that different, but to me the rewrite loses the charm of the original.
 
Youre making me have second thoughts again! So, what exactly is the difference? can you be more specific, or maybe point out some examples?
 
courant and john focuses more on analysis. Like mathwonk said, it is slightly pressured by its time to combine two subjects. Whereas the original is a full exposition on the calculus.
 
Huh? I thought mathematical analysis and calculus are the same thing..
 

Similar threads

"Introduction to Calculus and Analysis" by Courant & Fritz
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad What would a calculus author have to say on ##\int r^2dm##?
  • · Replies 11 ·
Replies
11
Views
4K
Undergrad A question regarding the ratio test for limits
  • · Replies 5 ·
Replies
5
Views
2K
Insights Precalculus, Calculus and Infinitesimals
  • · Replies 0 ·
Replies
0
Views
3K
Undergrad Analysis of functions of a single variable via multivariable calculus?
  • · Replies 10 ·
Replies
10
Views
3K
Insights What Are Numbers? - Insights for Beginners
  • · Replies 0 ·
Replies
0
Views
3K
MHB Book recommendations for self studying calculus.
  • · Replies 6 ·
Replies
6
Views
7K
Studying Should I read Introduction to Calculus and Analysis by Courant?
  • · Replies 3 ·
Replies
3
Views
2K
Insights What Are Infinitesimals – Simple Version
  • · Replies 5 ·
Replies
5
Views
3K
Other Complex analysis or calculus?
  • · Replies 15 ·
Replies
15
Views
3K