Greetings, I am an enthusiastic undergraduate university student in physics. In order to increase my mathematical knowledge and skills I would like to study a decent mathematical methods book. I came across two books whose names are: Mathematical Methods for Physics and Engineering by Hobson, Riley and Bence; Essential Mathematical Methods for Physicists by Weber and Arfken. I think the book by Hobson is more suitable, anyway I would like to hear your opinions on the topic. In addition to that how should I study them I do not get the change to ask the problems I struggle with to the instructors always? Thanks
I would get Arfken and Weber, but not the one with "essential" in the title. There's no reason to limit yourself in this case. I like their presentation of special functions, but their discussion of complex variables/contour integration leaves a lot to be desired. For that purpose, you can supplement with Wunsch - Complex Variables 3rd ed., it's pretty good. But that's just to learn math methods, if you want to learn mathematical physics, I would reccomend Szekeres - A Course in Modern Mathematical Physics and Hassani - Mathematical Physics. They present the same topics, but in a rigorous fashion. You'll learn about topology, functional analysis, measure theory, differential geometry, etc. Very good presentations in general and pretty pedagogical.
Well thanks for your suggestion but what is wrong with the Arfken's book having "Essential" in the title?
The Essential Mathematical Methods book is geared towards undergraduates. I was simply saying that it's not necessary to limit yourself to an undergraduate book when the graduate level book isn't anymore difficult. It just has some extra topics that were cut out of the undergraduate version.
If you want to learn new math I would disagree with Arfken. It is very challenging to learn new math from without a strong, strong background. A book that easier to learn from but at a similar level to Arfken is Hassani and the one I personally prefer.
Hassani has two books, one is rigorous mathematics dealing with topology, functional analysis, group theory, differential geometry, and the other is a math methods book that's between Boas and Arfken&Weber. So care must be taken when selecting which book to deal with.
Well, it depends on what you want to do. The rigorous one is a pure mathematics textbook motived by physical problems. So if you want to learn pure mathematics that are relevant to physics then choose that book. It's called Mathematical Physics. If you want to deepen your math knowledge relating to computational methods, then choose his math methods book, though I can't remember the title. Since you're an undergraduate you will probably benefit more from this book than his other one but again it depends on what you want to learn.
Ahhh I did not know he had two. After looking up both online I have only used the rigorous one but it does have a very good presentation of the topics.
Undergrad? First contact with maths? Boas it is! It's been one of the easiest books to learn from I've ever read. Once you've done boas you could go onto Hassani, it's quite nice too. Byron and Fuller is really a grad book and for that level of material you're better off reading a maths book rather than a methods book imo, you'll get a better insight into why. If I remember correctly, Byrona and Fuller does a bit of presenting theorems without proofs. I could be mistaking this for another book however..
I am pretty confused I already own Advanced Calculus by Hildebrand, and Advanced Engineering Mathematics by Kreyzig. I have yet to study some parts of these books. In addition to that I am especially curious about tensors, should I buy a seperate book on this topic or get one including the topic as a chapter, such as Arfken, Hobson etc.?
Get Boas for now. Arfken is more of a reference book for physicists. If you're really serious about learning more mathematics then the best book I've seen that teaches advanced mathematics to physicists is Baez's "Gauge Fields, Knots, and Gravity". Its an advanced book and you could at least be well versed in vector calculus, complex analysis, and differential equations before checking it out. Electromagnetism helps a lot too because the book's goal in the beginning is convincing you that EM in an example of a gauge field. The book focuses mainly on teaching you most of the mathematics used in theoretical physics that isn't taught to you during your undergrad. It gives a nice coverage of differential geometry, lie groups, and lie algebra with applications directly to physics that you would have seen before.
Tensors? Look no farther than this book here! http://www.math.odu.edu/~jhh/counter2.html This book is free and highly intuative and will give you a pretty decent introduction into the subject. If you mean the more algebray tensor producty notion of a tensor (although these are the same things as the once before) then maybe try the 2nd bourbaki book, Algebra I I wouldn't even touch this version of it unless you've already got some pretty good linear algebra under your belt though.