Mathematical Methods in the Physical Sciences

by Mary L. Boas

Now in its third edition, Mathematical Concepts in the Physical Sciences, 3rd Edition provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference.

This book is intended for students who have had a two-semester or three-semester introductory calculus course. Its purpose is to help students develop, in a short time, a basic competence in each of the many areas of mathematics needed in advanced courses in physics, chemistry, and engineering. Students are given sufficient depth to gain a solid foundation (this is not a recipe book). At the same time, they are not overwhelmed with detailed proofs that are more appropriate for students of mathematics. The emphasis is on mathematical methods rather than applications, but students are given some idea of how the methods will be used along with some simple applications.

Genres: Physics, Mathematics, Science, Textbooks, Reference, Nonfiction, Technical

864 pages, Hardcover

First published January 1, 1967

Reviews

[Robert · Rating 3 out of 5]

This was the recommended text for maths for my physics first Degree, as, it transpires, it is for many, many physics undergrads.

I didn't use it enough then but when I did I found it difficult. It felt like it didn't explain enough - which looking back means didn't have enough worked examples. It also covers an enormous amount of terrain for a single volume.

Now, I find it more useful - as a reference work. It probably isn't the best book for introducing the more advanced topics - they need whole books each - but for reminding oneself of forgotten but once understood topics? It can do that job.

[DJ · Rating 5 out of 5]

Mathematical methods courses have traditionally been the battleground upon which engineers and physicists perish in a frustrating struggle against black-boxed equations and their dying, depressed crypt-keepers known as applied math professors. In the realm of mathematical methods book for engineers and physicists, however, this is the "one book to rule them all". After painfully attempting two or three others, I finally discovered this stellar work on a recommendation from Griffiths' Electrodynamics.

Like Griffiths, Boas anticipates each confusing element of a concept and is sure to point out easy traps before its too late and you're panicking in your final because all your Fourier coefficients are zero. There is much more here than usually covered in a single mathematical methods course and that supplementary material will come in handy in the coming years as each of you progress from baby engineers and scientists to fully fledged Edisons and Einsteins.

This book conveys the joys and wonders of mathematics in a clear and precise way to those who need it just so the most: engineers and physicists.

This book will remain in my inventory for the long journey ahead and I look forward to all the chances I'll get in the future to consult her.

[Daniel Cunningham · Rating 4 out of 5]

This is a really solid review/overview of math for sciences, particularly physics (or engineering.) Basically, if you are a sophomore or junior undergraduate, this is all the math you have probably already (supposedly) learned, in a somewhat condensed form. If you have never done e.g. multiple integrals, Fourier series or transforms, or differential equations, this is probably not the book for you. I think it would be really hard to learn all those things, from the ground up, from this book. If, however, you have been through a set of calculus courses up through mutlivariable and differential eqs, then this is a great book precisely because it gives only quick quick coverage to theory and to basic breadth, and instead focuses on applying all that math you have been learning to prepare you to move through e.g. junior and senior level physics courses.

I give four stars because there are places where I did feel additional explanation -or additional worked examples- would be helpful. Like many books, it includes harder problems towards the end of each section: a few more worked examples of this relative complexity would make this a five star book. My two cents, anyway.

[Livresque · Rating 4 out of 5]

Well, this was my undergraduate text book on Mathematical Physics along with others. For fundamental understanding at the beginning, this is a great book to go by. Explanations and worked out examples are quite good. Although I would surely want more of those than they are.

[Tom Ritman-Meer · Rating 5 out of 5]

This was the recommended text for the core mathematics modules when I was an undergraduate at Warwick. Back then it was quite tough but still very useful as a reference. Recently I read it cover to cover and it really is one of the most enjoyable books I've read. Since it's essentially applied mathematics it doesn't get weighed down by the burden of proofs and so you simply get the beauty of the mathematics itself. The scope of this book is huge and it serves as an excellent primer to university mathematics, albeit rather lacking in proofs.

[Erickson · Rating 5 out of 5]

Forgot to close this book, used this as part of my TA duty for mathematical physics class in Spring 2019.

To be honest, I never took such a course before in my life, so having this course as teaching duty was nice. In fact, I think I never understood the subtleties behind Fourier cosine/sine transform and the usual Fourier transform (I could not remember now but when I taught it as a course I did understand it), so it was also personally enlightening.

I really like this book for its explicit examples and clarity. Note that one should not expect "proofs" out of this book, this is more like a handbook for performing computations. Depending on what you mean by proofs, every chapter in this book could easily take another book to make rigorous. In that sense I won't be asking too much. I would not see any reason to give any rating less than 5; it's comprehensive topic-wise and serves its purpose.

I should note that if someone were to look for similar but slightly more advanced text, there's another one by Arfken/Weber. I think Boas is friendly for someone as early as first or second year of undergraduates; Arfken/Weber probably could last longer, even towards graduate school.

[Samuel L. Jacob · Rating 4 out of 5]

Having read and practiced all the subjects covered by this book, I have to say that an astonishing amount of mathematics can be learned from this excellent piece. The physical applications of the methods are quite enlightning, making physical insight sprout from the dedicated student and intertwining it with the beautiful mathematical foundations on which it is built.

The reader should, however, be skilled in calculus, basic proof methods and have a decent basic physics background (knowledge in classical mechanics, electromagnetism, thermodynamics and even quantum mechanics will be valuable).

A mathematician may cringe at the lack of mathematical rigor and abandon the book in search of a more advanced book on mathematical physics; this will, almost certainly, make him miss the obvious point of the book - to build intuition for the mathematics that underlies physics. This intuition cannot be built by mathematical rigor, but only by diligent practice, curiosity and thought into these physical meaning of the mathematics.

[Sanjay · Rating 5 out of 5]

My beloved. One of the greatest books, if not the greatest, to learn mathematical tools for physics students.

[Dean · Rating 5 out of 5]

An ideal reference book for all realms of mathematical physics. Sure, you might need to supplement with other sources, but this book should always be the first stop for when you feel you need a quick review. I wish I had used it sooner.

[mghf · Rating 4 out of 5]

Kentang, membaca buku ini harus punya motivasi di setiap lembarnya. Enam bulan membaca hanya sanggup sampai Legendre Polynomials, dan akhirnya say goodbye pada 6 bab lainnya. Tida mengerti kenapa dosen berkata ketika dia pusing dia akan membaca buku ini T.T pusing ya lebi ena tidur Pak T.T

[Junipero Verbeke · Rating 5 out of 5]

Riveting. The adventures of Mr. Fourier, Bessel and Dirac through the plains of the « Calculus » are sure to keep you on the edge of your seat in this no-holds barred thriller.

[Adam Lantos · Rating 5 out of 5]

I was astonished about how good the examples are and about how much insight the author gives the reader! Pretty good book.
The only downside is that it does not prove important things sometimes. For example, the similarity of matrices relation is only "proven" through an example. Also, I found that at some point, the authors could explain things in more words to make them a bit clearer and more intuitive, although they do clarify everything through examples; I guess this is their way of explaining something and it gets the job done for most cases at the end of the day.
As far as great examples are concerned, this is the king. But for anybody-like me-wanting proofs and more mathematical insights (not only physical as this book provides in spades) I would also check out other books (like, say, one of Hassani's books).
Lastly, it must be noted that it contains A LOT of exercises, which is always a good thing.

[Jurvis · Rating 5 out of 5]

This was my bible for mastering applied mathematics. It's well-worn pages are now held together with duct tape on my shelf. Boas has a knack for creating illuminating problem sets to round out her succinct explanations. This is a good thing for dense youngsters (like myself) who don't get it as she makes it look so simple throughout each chapter. If you need a less direct lesson, turn elsewhere.

[Nicholas Bonham · Rating 4 out of 5]

Absolutely crucial for gaining a solid understanding of the fundamental math techniques required to earn a physics/engineering degree. Even after graduation I find myself intrigued by this book, reaching for it whenever I think I could brush-up my math skills a bit.

[Arman Behrad · Rating 4 out of 5]

I will definitely consider this huge piece of mathematics as my future reference.
Two first season was amazing, but I felt rigidity in ordinary and partial differential equation chapters.
Maybe a little more intuitive explanation of ‘Transforms’ would be more comprehensive.

[Pavel Fedorov · Rating 5 out of 5]

Very self study friendly, gives a flavour for many useful topics you will really need..,lots of practice problems and solutions… you don’t necessarily need any physics or engineering background for 99 percent of it, best book to learn some practical math if you don’t already know it

[Hary Mulyadi · Rating 5 out of 5]

Great Book!. Comprehensive mater contents. It describe from simple calculus to the math for quantum and analytic physics.

[Caleb · Rating 2 out of 5]

Not a big fan of this textbook. The practice problems are good, but I found many of the explanations unintuitive, and in some sections it was as if there was missing information that may have felt obvious to the writer, but was crucial to having the concept click for me. It is probably better used to review information than to learn from; that is to say, it's probably quite good if your professor integrates it tighter into the class, but it's bad as a supplemental material for independent study. I'd recommend the Openstax Calculus 3 text instead or in parallel. It's not a perfect overlap, but both books share most of the same mathematical concepts and the Openstax one is much friendlier to someone new to these topics.

[Nathaniel Claus · Rating 1 out of 5]

This book is garbage. Buy a different mathematical physics book if you’re new to this material. It seems to assume you already have a grasp of the material, especially in subjects like linear algebra and others. Examples are rushed through, the descriptions suck, and overall it doesn’t prepare you to solve the problems for each section. This book could be good as a reference for someone with more mathematical experience but for learning the math this is garbage.

[Soumyaneel Manna · Rating 3 out of 5]

Though this book has concise coverage on major portions of Mathematical Methods, it lacks depth and most derivations and proofs have been done in weird, discontinuous and too-much-reference manner. Most derivations and proofs have been done in shortcuts and most theories have been explained with crooked examples which will make you more confused.

[Pollopapas]

Aparece la inversa de la transformada de Laplace como la integral de Bromwich.
The inverse Laplace transform is

\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}e^{zt} L(f)(z)dz, t>0

Esta "fórmula" se deduce considerando a la transformada de Fourier como inspiración

[Astral · Rating 3 out of 5]

In general it is a good book. However, could be much better if it had more examples and exercises. Some of its concepts are really hard to digest as they are briefly explained e.g Special Functions. Still waiting for the day for someone to write a math book that could everyone understand easily.

[Heather · Rating 5 out of 5]

I have nothing but love for this book. I have retrieved it several times since it was needed for studying for practical applications in research and analysis. The examples are excellent and well explained!

[Rose · Rating 3 out of 5]

read: series, complex numbers, complex analysis, linear algebra, ODEs, series solutions to ODEs, fourier and laplace transforms, PDEs

conclusion: too much too fast; good way to get a conceptual idea of new fields of math without actually learning how to do said math.

[Big Endian · Rating 2 out of 5]

A very terse book on mathematics for physics. It was the main mathematical text for my degree, and I probably touched it only once or twice. At least for me, it just doesn't go into enough explanatory detail.

[Lam · Rating 5 out of 5]

I really love this book. This is literally 5/5 because:
- easy to understand
- so intuitive

It feels like I can read it while doing something, and it is just, fun. This is the #1 of my fav academic books from my uni years.

[Muhammad Siddique · Rating 5 out of 5]

good books

[Jaewoo · Rating 4 out of 5]

12장까지만 읽음

[Iqbal Andryan · Rating 2 out of 5]

Unclear steps. Giving confusing ways to solve the problems.

[Ellie White · Rating 2 out of 5]

differential equations make no sense to me