A question about strange claims in some textbooks

Hello respected member
To those who reached by this message, I hope it finds you all well.

When I was wandering and skimming some textbooks -as I usually do to get some insight and plan my future studying- I came across a textbook which made some very strange claims, its called the physics of waves by Elmore and Heald, well first of all it seems to me an excellent textbook because of some thing upon which I have judged it.
- It contains everything about waves as far as I know.
- It has a lot of problems, and most importantly they are give after each section, not like some other textbooks which prefer to give you miscellaneous problems on all the sections of the chapter at the end of it, which may confuse the reader (In my humble opinion).
- I think it is very well organized.
... etc

However, at the preface the textbook claimed that the textbook requires only one year of calculus as math. prerequisite, but when I skimmed the textbook I have found that the textbook do use appallingly more math that it claimed, based on my skimming I have found the following math used in it:
- ODEs.
- PDEs.
- Special functions (like Bessel).
- linear algebra (or matrix operations I don't know the difference between the two by the way).
- Complex variables.
- Tensors.
- Fourier series.
- Vector analysis.
- WKB approximation (I am not sure if this is a math of not, I included it since it came many time when I skimmed math methods textbooks).
- Frensel integrals.
- Fourier transform.
Well, but this is based only on a quick skimming, maybe I will find much more if I studied it.
So my question is how can the authors make such a claim?!! and if anyone can make these claims, then well, shall we take their words seriously?

Thank you.

You are expected to study the mathematics as you proceed through the book.

The effect is called the imposter syndrome.
An expert doubts their own ability, and overestimates the ability of those who follow.
https://en.wikipedia.org/wiki/Impostor_syndrome

Baluncore said:

You are expected to study the mathematics as you proceed through the book.

The effect is called the imposter syndrome.
An expert doubts their own ability, and overestimates the ability of those who follow.
https://en.wikipedia.org/wiki/Impostor_syndrome

Won't they face legal consequences, should someone press charges?
Also isn't the syllabus for "1 year of calculus" more or less similar in different courses?

Aurelius120 said:

Won't they face legal consequences, should someone press charges?

Charges of what?
Only in the USA.

What the authors specifically say is


which sounds reasonable.

Frabjous said:

What the authors specifically say is ...
which sounds reasonable.

Very reasonable. It is permitted to learn mathematics in a physics course. In fact, it is very common to do so.

Baluncore said:

Charges of what?
Only in the USA.

IDK People sue for much less. But having read this:

Frabjous said:

What the authors specifically say is

View attachment 339153
which sounds reasonable.

Yes this is good

Frabjous said:

What the authors specifically say is

<<skipped image from the textbook>>

which sounds reasonable.

Well first of all I agree with you totally about what you have mentioned about the fact that students may learn some math along the way while reading physics textbooks, that's unquestionable. However, I still think the claim made by the book still counterproductive, because the book requires too more math than suggested in the preface.

Now, is not it the same if Jackson suggested in his preface that his book requires calculus 1 and 2 and some other easy peasy math? Yes, Jackson in way too hard, but I think the idea I want to explain is clear.

If you looked at the list, I have written you will find that the math needed for understanding the book requires many times the time needed for the physics, actually it almost covers all the math studied at a physics undergraduate program, this I don't agree with the author of the textbook in his claim and I think it will lead to a mental catastrophe for anyone who want to study the textbook by himself.

But what is the mathematics which shall be suggested by physics textbook's authors? I think the math needed is what makes the textbook in the region of the zone of proximal development, or ZPD suggested by the Vygotsky (https://en.wikipedia.org/wiki/Zone_of_proximal_development), which in the case of this book, vector analysis, ODEs, PDEs, linear algebra, complex variables, Fourier series and transform. You can notice that even in this case the learner still need to study some other math (which is a lot by the way).

I think the claim that such a student can learn such a textbook in the time suggested by the author (2/3 of the book in a semester) which of course will include many other subjects is impossible for a student who know only calculus 1 and 2.

Lastly, I considered the textbook's prefaces is a valuable source of information about the textbook, but know I became more cautious about this.

gmax137 said:

Very reasonable. It is permitted to learn mathematics in a physics course. In fact, it is very common to do so.

I agree, but not this much of math.

Distinguishing between physics and applied math can be difficult. One will not go very far in physics without learning math as one learns the physics. You are being self limiting.

I am wondering what the problem is.

The thread title is "strange claims in some textbooks."
Then we find out it's one claim in one textbook.
Then we find out that it's not so much a "claim" as a pedagogical approach, and it's not even really what the OP said it was if you read the following paragraph.

So what's the problem? If the OP finds this one book unsuitable, pick another.

Vanadium 50 said:

I am wondering what the problem is.

The thread title is "strange claims in some textbooks."
Then we find out it's one claim in one textbook.
Then we find out that it's not so much a "claim" as a pedagogical approach, and it's not even really what the OP said it was if you read the following paragraph.

So what's the problem? If the OP finds this one book unsuitable, pick another.

Well, first of all yes, it is just one claim in one textbook, if you want me to include some other textbooks, I will be able to do so, but after I pass over some textbooks I have skimmed previously. However, I think the idea I wanted to explain will remain the same, which is about some misleading guidance provided by some authors (at least misleading in my opinion).
There are many other better ways to give a better guidance in a textbook so that students can choose if the textbook is suitable for them or not... I can say more generally that in many cases I have noticed that some textbooks authors extremely underestimate the prerequisites needed for studying their textbooks.
Lastly which is most importantly, the problem is not that I cannot change the textbook if it is not suitable for me... but the problem raised because I consider textbook's prefaces as one of the important criteria for determining whether the textbook is suitable for my needs or not, but this textbook like some other ones makes one of these criteria entirely not useful.
I will include some of these criteria I am using to determine the usability of any textbook for my needs (although I want to make this a separate thread in future, because I think this discussion may become lengthy, and the topic is too important for me... anyway, they are:
- Textbooks prefaces.
- Discussions of professors I find on the internet, including a lot of this in this forum.
- Reviews on educational journals.
- Some reviews professors publish on their websites.
- Previewing (if I couldn't choose between some textbooks which is better for me based on the previous criteria).

I hope the previous can explain why I felt annoyed about the guidance provided by the textbook.

@Florian Geyer are you self-learning? Or are you looking to supplement the textbooks assigned in class? Self learning is a very tough way to go.

I may also need to add that the textbook is taught in the university of the author after a semester of classical mechanics (I think for the juniors more than sophomores), those students will not face any problem with the textbook since they will have at last studied ODEs, PDEs, vector analysis, linear algebra, some transforms, and of course some complex variables, thus they will be able to catch up even if they needed some new math to learn along the way... they haven't studied only calc 1 and 2. thus it is misleading to include this in your preface of your textbook!!

gmax137 said:

@Florian Geyer are you self-learning? Or are you looking to supplement the textbooks assigned in class? Self learning is a very tough way to go.

Nope I am a self learner, and I will never be able to afford any college degree tution in the advanced world, but I am still doing great in my journey.
btw I am not entirely self-learner, since I watch lectures from Youtube, thus you may considr me scaffolded self-learner.
I have learnt some language entirely by myself, thus I think I will be able to do so even with physics.
I had many dicussions about the hardships of self-learning, I know this well.

How is this misleading? He says the starting point is calculus, and then the mathematical sophistication increases. Your complaint is that the mathematical sophistication increases beyond calculus.

This may not be what you want, but misleading?

Vanadium 50 said:

How is this misleading? He says the starting point is calculus, and then the mathematical sophistication increases. Your complaint is that the mathematical sophistication increases beyond calculus.

This may not be what you want, but misleading?

Well, the textbook used ODEs and Fourier series, and complex numbers in chapter 1, in chapter 2 it used some double integrals (calculus 3) and some vector analysis, and Bessel function... all this is mixed together with the complicated physics in the textbook... I think it should just stated this clearly in his textbook. The misleading part is stating that a student can start studying it if he studied only calc 1 and 2.
I don't have problem with the textbook itself, I have problem with the strange claims in the preface.
The author should state clearly the math needed for his textbook nothing more nothing less.

I just looked at a bootleg copy of Chapter 1. I would certainly have been able to handle it after 18.02 (MIT's 2nd semester calculus). When they introduce new math, they introduce it - they don't expect the reader to know it already. And while the wave equation is a differential equation, it does not require the usual machinery taught in a DiffyQ class to solve, and besides, a book on waves without the wave equation would be pretty useless, don't you agree?

Rather than being "misleading", I think it is more likely you overestimate where your self-teaching has gotten you. That's something that probably should be addressed, but hardly the book's fault.

And we're still talking about just one book.

Vanadium 50 said:

I just looked at a bootleg copy of Chapter 1. I would certainly have been able to handle it after 18.02 (MIT's 2nd semester calculus). When they introduce new math, they introduce it - they don't expect the reader to know it already. And while the wave equation is a differential equation, it does not require the usual machinery taught in a DiffyQ class to solve, and besides, a book on waves without the wave equation would be pretty useless, don't you agree?

Rather than being "misleading", I think it is more likely you overestimate where your self-teaching has gotten you. That's something that probably should be addressed, but hardly the book's fault.

And we're still talking about just one book.

Aha, I understand your point of view now, thanks.

Regarding my self-study, well, I am a freshman right now, I have only studied physics for about 3 months. (I think I have to defend myself )

French‘s Vibrations and Waves might be a better fit for you.

This is not a question of math, but of sophistication, and right now you are essentially a first semester freshman.