Which of these should I begin with?

[AdamA0]

I have these two textbooks:
Mathematical Methods in the Physical Sciences
https://www.amazon.com/dp/0471198269/?tag=pfamazon01-20
And
Elementary Linear Algebra
https://www.amazon.com/dp/1118473507/?tag=pfamazon01-20
Which should I begin with? And for the linear algebra textbook, is it all useful for a physicist? I mean, should I work through it all?
EDIT: I think I should mention that I finished all calculus courses, along with ODE and PDE courses. A lot of the material in the first book is already familiar.

 

[ShayanJ]

Start with Boas' textbook.
No, You don't have to study linear algebra in that depth. It may be useful some time in the future but its not necessary now. But to learn linear algebra as a physics student, its enough to study the math chapter of Shankar's or Ballentine's textbooks on QM.

 

[AdamA0]

Start with Boas' textbook.
No, You don't have to study linear algebra in that depth. It may be useful some time in the future but its not necessary now. But to learn linear algebra as a physics student, its enough to study the math chapter of Shankar's or Ballentine's textbooks on QM.

Is Baos' chapter on linear algebra enough?

 

[ShayanJ]

I didn't know it has a chapter on linear algebra!
Anyway, it doesn't seem to be enough but its a good place to start.
I should also say that Boas' book is a good book but it seems elementary to me. I think its better that, after finishing it, you deepen your knowledge by reading Arfken's.

 

[dfan]

Linear algebra is fundamental to quantum mechanics, so you definitely want to learn it well. I feel like I had a big leg up in my QM courses by already being very familiar with linear algebra. If you have learned other topics from Boas you can learn the fundamentals of linear algebra there as well, but be aware that it's a semester's worth of material crammed into one chapter. Introductory quantum mechanics courses usually present the necessary linear algebra as they go, so already having had some background with the ideas will already be enough to give you some advantage over students being exposed to the concepts for the first time. If you're actively interested in the topic, by all means learn more. The Elementary Linear Algebra textbook you linked to doesn't look that promising, though.

 

[mpresic]

I respectfully but completely disagree with Shyan. A strong background in Linear Algebra I learned as a sophomore was indispensable in taking later Junior- and Senior level physics courses, graduate courses and doctoral qualifying exams. Mechanics, Quantum Mechanics, and to a lesser extent the other subfields all require it. Boas's book is important too, but it should be examined later. A good background in linear algebra will enable you to spend less time reviewing the linear algebra put forth by Shankar and other authors. Shankar presents the linear algebra (in infinite dimensions) to Yale physics graduate students assuming they had a strong background in linear algebra.

A complete understanding of powerful mathematical tools makes it easier to learn physics, not harder.Boas's book is not as complete as (say) Morse and Feshbach, but I think it is about as complete as Arfken and Weber, and much more readable. No one could expect to learn the material in Morse and Feshbach in one or two semesters (the time allotted Mathematical physics in most graduate schools).
I do warn the physicist to beware. There are many aspects of the proofs of the theorems in linear algebra which are less important. The same could be said for proving Rolle's theorem or the intermediate value theorem in Calculus (Analysis) to a physicist. Nevertheless, proofs are necessary in training of a physicist to present a convincing case as to the correctness of the mathematics.

 

[MidgetDwarf]

I took a LA course from that book. The book is better than a lot of other books at this level. I strongly prefer it over Strang and Lay.

The problem with this text is that some sections can be extremely unclear. Linear Operators and Transformations portion of the book is hard to read for beginners in my opinion. Some theorems lack examples.

Some sections are overcomplicated, such as, change of basis, Linear Transformations, and the section of spanning

Spanning is really easy, but the book is not clear whether in the examples the author used row or column vectors.

With all its faults, the book is good. Not sure how useful for a physics students. The problems range from plug and chug to theory.

Vector spaces are explained nicely.

I am currently reading Friedberg and a lot of the questions or topics i did not truly understand, are becoming clear with Friedberg.

Get an older edition. There is a free pdf floating around uploaded by a university on the web.

 

[MidgetDwarf]

If you decide to purchase this book supplement it with another book. LA is a lot different than Calculus or ODE for that matter. In LA you will be presented with atleast 5 things every sections. These 5 things are usually theorems or definitions. So you have to take your time and play around with it and truly understand what these objects mean.

When starting the vector spaces portion, I would read a short article about sets and properties of numbers. Ie odd,even. Difference between an Integer, Irrational, Rational number etc. Will make the problems in the section approachable.

I had a teacher that would fill up the chalk board and walk out, and this information helped me out a lot while learning vector spaces.