# Error in Mathematical Methods for Physicist by Arfken, et al

• jinjung
In summary, the conversation discusses the book "Mathematical Methods for Physicist: A Comprehensive Guide (Seventh Edition)" by George Brown Arfken, Hans Jürgen Weber, and Frank E. Harris. The speaker mentions reading up to page 35 and finding three errors in the content related to infinite series and the binomial theorem. However, they do not have any specific questions and remark that errors in textbooks are common.

#### jinjung

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.

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!)

## 1. What is the main purpose of "Mathematical Methods for Physicist" by Arfken, et al?

The main purpose of "Mathematical Methods for Physicist" is to provide a comprehensive and rigorous introduction to the mathematical techniques and methods used in physics. It covers a wide range of topics including vector calculus, complex analysis, differential equations, Fourier analysis, and more.

## 2. Is this book suitable for beginners in physics?

While "Mathematical Methods for Physicist" is a valuable resource for physicists of all levels, it is primarily designed for advanced undergraduate and graduate students with a strong mathematical background. Some prior knowledge of calculus, linear algebra, and differential equations is recommended.

## 3. How is the content of this book organized?

The book is organized into 14 chapters, with each chapter covering a specific mathematical topic. The first few chapters provide a review of basic mathematical concepts, while the later chapters delve into more advanced topics such as tensors, group theory, and special functions. Each chapter also includes examples and practice problems to reinforce the concepts.

## 4. Are there any solutions or answer keys available for the practice problems?

Unfortunately, the book does not include solutions or answer keys for the practice problems. However, there are many online resources and study guides available that provide solutions and explanations for the problems in the book.

## 5. Is the content of this book applicable to other fields of science?

While the book is primarily geared towards physics, many of the mathematical techniques and methods covered are applicable to other fields of science such as engineering, chemistry, and astronomy. The book also includes examples and applications from various scientific disciplines to demonstrate the relevance of the mathematical concepts.