Error in Mathematical Methods for Physicist by Arfken, et al

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Discussion Overview

The discussion centers around perceived errors in the textbook "Mathematical Methods for Physicists" by Arfken et al., specifically focusing on mathematical preliminaries and the binomial theorem. Participants examine specific equations and exercises, raising concerns about their accuracy and implications for understanding the material.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant identifies three errors in the textbook, including an incorrect inequality in Equation 1.15, missing prerequisites in Exercise 1.1.7, and issues with the binomial theorem in Equation 1.66.
  • Another participant questions the purpose of the thread, suggesting that errors in textbooks are common and not unusual given their complexity.
  • Some participants speculate that errors might be intentional to engage readers, although one participant expresses skepticism about this idea, citing pedagogical concerns.
  • A participant reflects on their own experience with the textbook, suggesting that earlier editions may have contained even more errors, contributing to confusion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the nature or significance of the errors. While some acknowledge the possibility of errors, others debate their implications and whether they might be intentional.

Contextual Notes

Participants express uncertainty regarding the impact of the identified errors on the understanding of the material and the overall reliability of the textbook.

jinjung
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Mathematical Methods for Physicist: A Comprehensice Guide (Seventh Edition) by George Brown Arfken, Hans Jürgen Weber, Frank E. Harris

I am studying it.
Up to now I read to page 35 and have found 3 errors.

Chapter 1 Mathematical Preliminaries
1.1 Infinite Series
More Sensitive Tests
Equation 1.15 (Page 8)
≤ is incorrect, < is correct.

Exercises 1.1.7 (Page 11)
It must be given to prerequisite that p > 0 and q > 0

1.3 Binomial Theorem
Equation 1.66 (Page 34)
If n > m, m(m - 1)...(m - n + 1) = 0
In other words, whether n → ∞ or not, the remainder is always 0.
Furthermore, the radius (interval) of convergence is not -1 < x < 1.
Because m(m - 1)...(m - n + 1) = 0, ratio test fail.
As far as either m or x does not approach infinity, the power series is convergent.
 
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I don’t get the point of this thread. Do you have questions regarding these issues? Otherwise errors in textbooks are nothing new as it is essentially impossible to write an error-free text. In particular one with the size of Arfken.
 
Maybe the errors are deliberate. Put there to make sure you're paying attention.
 
Jehannum said:
Maybe the errors are deliberate. Put there to make sure you're paying attention.
Being a textbook author myself, I seriously doubt this. It would be quite non-pedagogical.
 
I imagine the edition I used (back in the day) had even more errors. (No wonder I'm so confused!)
 

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