Question on the Boas Math Methods book.

[Mathemaniac]

I'm going to pick up a math methods book to beef up my more physicsy math, as it were, since the math program at my school is less geared to physics and engineering and more towards education, business, and computer science (and the physics program itself is falling apart).

All the rage seems to be around the Boas book. So I looked it up on Amazon and found that in the used and new section I can get 2e for about fifteen bucks, while I can't get the 3e for less than seventy.

Is there a significant difference between these two editions that would warrant the investment in the third edition when I'm just going to use it for some casual self-study?

 

[lzkelley]

The differences between the two are subtle; as usual, its mostly the numbers of problems etc etc etc. No important differences.

Also, i spent a year using the Boas book - and its absolutely awful; like very awful. At the same time i have also heard that its significantly better than most other math methods books... so maybe there's just no such thing as a good one.
Cheers

 

[George Jones]

Also, i spent a year using the Boas book - and its absolutely awful; like very awful. At the same time i have also heard that its significantly better than most other math methods books... so maybe there's just no such thing as a good one.
Cheers

I know opinions about books are very subjective and personal, but I am curious: what didn't you like about Boas?

 

[MathematicalPhysicist]

For a rigorous acount with no exercises, try hilbert's and courant's 2volume text, if you need just to know how to solve it without understanding why, then Arfken is better than Boas, for example in the green functions area Boas' book is lacking it just gives examples without concrete algorithm of how to solve green functions problems, Arfken gives it.

 

[Mathemaniac]

Interesting responses. Looks like the 2e might be a preferable deal, should I go with Boas.

I heard in a variety of places that Boas was the math methods book to have, and anyone studying physics ought to have a copy. The reviews on Amazon.com were generally positive as well. I might look up Arfken though; for now I'm mostly interested in learning to to solve the problems and practicing them.

Has anyone tried Kreyszig's math methods book? A buddy of mine used that in his math methods class and he absolutely loves it. Judging from the name, it seems more engineering-oriented.

 

[xristy]

Sadri Hassani's "Mathematical Physics" is a balance of rigor and many worked examples. Included are an extensive discussion with examples of Green's functions and group theory, manifolds and Lie groups.

I have no experience with Boas.

 

[lzkelley]

I think the discontinuity between my opinion of boas - and the general opinion is as follows:

For the most part, a physicist will use a math methods book to look up some obscure detail that they're not especially interested in (because they're not a mathematician, however close) --> i.e. they'll look up something, read a few lines, and use an equation or method etc. I can imagine that working well with boas - its incredibly densely packed with information, and includes an immense array of topics.
When i was using boas, we were working through it - page by page, in which case boas' methods are somewhat lacking. She often goes into detail on easier steps, then takes huge leaps on complex ideas with hardly an explanation. Also, when a student is reading through the book to learn a topic they're not familiar with - she doesn't provide enough information, or enough examples.

Anyway, it sounds like overall you're looking for a book that should be more qualitative and less intense. Maybe take a look at the other peoples alternative recommendations?

 

[ice109]

i think in general all these books are a terrible idea.

 

[Kurdt]

I have Kreyszig and Boas. I like both books, but if you only want one I'd side with Kreyszig because its better value for money.

 

[ZapperZ]

I think the discontinuity between my opinion of boas - and the general opinion is as follows:

For the most part, a physicist will use a math methods book to look up some obscure detail that they're not especially interested in (because they're not a mathematician, however close) --> i.e. they'll look up something, read a few lines, and use an equation or method etc. I can imagine that working well with boas - its incredibly densely packed with information, and includes an immense array of topics.
When i was using boas, we were working through it - page by page, in which case boas' methods are somewhat lacking. She often goes into detail on easier steps, then takes huge leaps on complex ideas with hardly an explanation. Also, when a student is reading through the book to learn a topic they're not familiar with - she doesn't provide enough information, or enough examples.

Anyway, it sounds like overall you're looking for a book that should be more qualitative and less intense. Maybe take a look at the other peoples alternative recommendations?

However, in defense of Boas, you need to look at the intent of her book that she laid out in the Preface (2nd Ed.):

1.

This book is particularly intended for student with one year of calculus who wants to develop, in a short time, a basic competence in each of the many areas of mathematics needed in the junior to senior-graduate courses in physics, chemistry, and engineering.

2.

It is the intent of this book to give these students enough background in each of the needed areas so that they can cope successfully with junior, senior, and beginning graduate course in the physical sciences. I hope, also, that some students will be sufficiently intrigued by one or more of the fields of mathematics to pursue it further.

3.

Scientists, even more than mathematicians, need careful statements of the limits of applicability of mathematical processes so that they can use them with confidence without having to supply proof of their validity. Consequently I have endeavored to give accurate statements of the needed theorems, although often for special cases or without proof. Interested students can easily find more detail in textbooks in the special fields.

What she intended to do was to make sure that you did not see the phrase "orthonormal" or "eigenvalues" for the first time in a physics class. For many of us, we had to learn the mathematics at the same time as the physics. This is something she's trying to avoid. But this means that she has to deal with students who are still early in their undergraduate years with limited mathematics sophistication. That is why the book has to be, in many instances, superficial in some of the depth of the material being covered, and as she has said, covered only special cases. Many of these special cases are what physics and engineering students would have seen or will see, such as heat conduction problems and Gauss's law. It is also why this text is less "advanced" than say, Arfken text. But for the target audience and target purpose of what she's trying to accomplish, I don't know of any better text than this.

Zz.

 

[Mathemaniac]

Thank you all for the responses. Considering the debate here, I'm probably even more at a loss as to which is preferable!

ZapperZ: Actually, you're one of the reasons why I was looking closely at Boas. Having almost finished a math degree, among the classes beyond calculus that have a lot of physics applications, I've had Linear Algebra, ODE, Multivariable Calculus, and Numerical Analysis. There's still a lot I don't know, however: vector/tensor calculus, Fourier analysis, PDE, and probably a bunch of other stuff whose existence I'm largely unaware of (some of this stuff I'll be getting next semester in Advanced Calculus). Would Boas still be appropriate for me? In spite of it being less "advanced," I can't imagine it's a math methods book for dummies or some such thing.

What I primarily need is a book that is good for self-study. Of course, I'm not particularly interested in a lot of rigor at the moment. Essentially I need something with a lot of worked examples as well as problems with back-of-the-book answers.

I might just go ahead and get the second edition of Boas, just because it's only fifteen bucks (in the used/new section on Amazon). Then I can get Kreyszig or something along side it. But alas, I'm on a budget here, and I'm also looking at getting a couple other books in QM and E&M.

The Amazon.com reviews of Arfken aren't particularly positive; it seems to have a reputation for being nothing more than encyclopedic (not that Amazon.com reviews are necessarily exemplary, but it's something to think about). I'm not in any immediate need of an encyclopedia; my CRC Math Tables book has yet to fail me when I'm in need of something.

 

[George Jones]

i think in general all these books are a terrible idea.

Why?

What book(s) do you recommend?

 

[ZapperZ]

Thank you all for the responses. Considering the debate here, I'm probably even more at a loss as to which is preferable!

ZapperZ: Actually, you're one of the reasons why I was looking closely at Boas. Having almost finished a math degree, among the classes beyond calculus that have a lot of physics applications, I've had Linear Algebra, ODE, Multivariable Calculus, and Numerical Analysis. There's still a lot I don't know, however: vector/tensor calculus, Fourier analysis, PDE, and probably a bunch of other stuff whose existence I'm largely unaware of (some of this stuff I'll be getting next semester in Advanced Calculus). Would Boas still be appropriate for me? In spite of it being less "advanced," I can't imagine it's a math methods book for dummies or some such thing.

I would think that yes, it is still an appropriate book. The chapter on calculus of variation alone is worth getting the book. It also provides to you a "survey" of various aspect of the mathematics that someone in physics/physical sciences/engineering would encounter, not just in terms of the areas of mathematics, but also in the form that they encounter them, since she some time tackle those special cases.

What I primarily need is a book that is good for self-study. Of course, I'm not particularly interested in a lot of rigor at the moment. Essentially I need something with a lot of worked examples as well as problems with back-of-the-book answers.

This would be the book. If you get the Student's Guide text, she even explains in detail the answers to a few of the problems.

Zz.

 

[ice109]

Why?

What book(s) do you recommend?

because they're adhoc collections of a ridiculous amount of mathematics.

i recommend taking the classes that teach the material in a linear fashion.

 

[mgiddy911]

because they're adhoc collections of a ridiculous amount of mathematics.

i recommend taking the classes that teach the material in a linear fashion.

This is good in theory but in practice I don't know?
Does one have the time to take a class on PDE, Fourier, Tensor Analysis, Calculus of Variation, Special Functions, Complex Analysis, Real Analysis, Probability, and Linear Algebra?
All such that the material is covered slowly in a linear fashion? I think the one main reason these books exist is because dept's have to offer classes called Mathematical Methods in Physics to prepare their students. However often due to time constraints these classes are bunched into one semester so All the above topics need to be touched upon briefly, or some need to be left out.

I think many students do not have the time to study all of those topics rigorously. Especially if they go to a school where more than just their major classes are required, ie. humanities classes.

To the OP.
I like Boas book as a reference, not not as much as a learning source. If I was not taking a class in Math Methods currently then I would find Boas cumbersome. Also, some may not condone this however, if you check ebay, you can generally find cheap copies of the international or economy editions. I have one for Boas and one for Griffiths E&M as I was in a bind for cash this semester. Search ebay for the book title and you may find for instance a copy of boas for $25 then if you look at the listin you'll see it is comin form new delhi india, and is not the American edition but the economy edition, however there is very little difference between the two. It will be paperback, and cheaper quality paper and black/white printing only.

 

[ZapperZ]

because they're adhoc collections of a ridiculous amount of mathematics.

i recommend taking the classes that teach the material in a linear fashion.

I agree with what mgiddy911. This is a rather empty statement. The reality is that many physics majors do not havethe patience nor the capacity to take ALL of the mathematics classes that is needed. Think of how many classes they have to take. Without such text, they would have learned the mathematics by themselves WHILE taking the physics classes. This is the better alternative? I don't think so.

Rather than simply criticizing the nature of the book, ask if the book is effective in doing what it is supposed to do. From what I've gone through, and what I have observed, it is a very useful book.


Zz.

 

[Mathemaniac]

because they're adhoc collections of a ridiculous amount of mathematics.

i recommend taking the classes that teach the material in a linear fashion.

My university doesn't offer all of that math, and even if it did, it would hardly be practical. When I transfer, I want to get through a physics degree as fast as I can. As it is, I'm already likely going to have spent a total six-and-a-half years as an undergrad. Sure, in the mean time, I take what classes I can get, but there's a ton of exotic mathematics needed for physics that I can't get here.

I did go ahead and purchase the second edition of the Boas book (and some other math/physics books), which arrived in the mail a couple days ago. After all, I only had to spend fifteen bucks on it. I'm thus far pleased with what this book has to offer (I won't be able to really dig in until finals are over, though).

 

[matqkks]

If you are looking for a book that assumes very little knowledge of mathematics and prefer to learn by yourself then 'Engineering Mathematics through Applications' by K. Singh is an excellent book. It gives lots of examples from fields such as electrical principles, control theory, mechanics etc. It also has complete solutions to ALL the problems in the book on the book's website at http://www.palgrave.com/science/engineering/singh/
There are also some sample material on this web site. Check it out!

 

[gulaman]

If you're going to try Arfken...

We're using Arfken for most of our mathematical physics classes here in the Philippines...
Using it with other math methods books would be helpful for self-study... Arfken is not that thorough in his discussion so you might like other referneces with it...

Kreyszig is good for linear algebra... simple explanations for matrices, and vector analysis...