Mathematical Physics textbook advice?

[Coto]

The recommended textbook for this mathematical physics class is Mathematical Methods for Physicists by Arfken (http://www.amazon.com/dp/0120598760/?tag=pfamazon01-20), however I've read some reviews online that seem to think that this textbook is inferior to the textbook Mathematical Physics: A Modern Introduction to its Foundations by Hassani (http://www.amazon.com/gp/product/0387985794/?tag=pfamazon01-20).

Does anyone have any experience or feedback on these two books? How similar they are? Which is better for learning as well as reference?

The course description is:
"Application to problems in physics of method of steepest descent, Fourier and Laplace transforms; boundary-value problems, integral equations, and Green's functions. "

I know it's a bit vague, but perhaps will give a glimpse as to which book may be more appropriate. The Arfken text is not required by the course, only recommended.

Thanks in advance, Coto.

 

[daveb]

I have used both books. The Arfken text is a great text for the standard undergrad physics classes, but I found Hassani to be better suited for graduate classes (my graduate mathematical physics class used Hassani). The Arfken book could also be used for graduate classes, but the Hassani book has a more advanced view on the mathematics.

 

[ice109]

right now I am reading this

https://www.amazon.com/dp/0521054265/?tag=pfamazon01-20

and I'm only 12 pages into but i like it a lot because it's from a pure math perspective so it is pretty much as rigorous as you can get. meaning it assumes very little and proves everything, akin to beating a dead horse but i like that cause i like math and i ask too many questions so i need everything proven.

 

[proton]

I've heard the book by Boas is the best math methods book. Its not as mathematically rigorous as the others, so physis majors may like it more

 

[thirdchildikari]

I've heard the book by Boas is the best math methods book. Its not as mathematically rigorous as the others, so physis majors may like it more

I'm taking a Math Methods of Physics course this semester as a junior physics major, and this is our required text (Mathematical Methods in the Physical Sciences by Mary L. Boas, 3rd edition). I love it so far.

 

[thirdchildikari]

I just thought I'd throw in here that the other day in class we were trying to figure out how to calculate curl in spherical coordinates, and Boas only has cylindrical coordinates. Kinda disappointing, considering some of the questions in the text would me much easier to solve in spherical, rather than converting everything to Cartesian.

 

[Coto]

So I managed to borrow a copy of Arfken, and I shelled out the money for the Hassani. I've worked from both now, and I'm not really a fan of Afrken. I will admit, his book is definitely geared towards the notation that was taught in 1st and 2nd year mathematics, and there are a few more examples, and a few less theorems, and proofs etc. But Hassani is actually a pleasure to read. It has well written bio's of different great scientists relevant to that topic (i.e. Green's Functions --> bio about Green)

Further, at this level of physics, we've encountered Dirac's bra-ket notation of vectors in QM, as well as some of the more formal useful notations used in this book. Why delay the inevitable? The newer notations used in this book, are used because they are more powerful then the old notations. Eventually we're going to need to know this stuff. The mathematics is the same behind it, it's really just a matter of wrapping your head around the formalism.

So go Hassani!

 

[MathematicalPhysicist]

well i haven't yet read neither, but if you want the classic book, i think the one by hilbert's and courant's is a must have.

 

[George Jones]

I just thought I'd throw in here that the other day in class we were trying to figure out how to calculate curl in spherical coordinates, and Boas only has cylindrical coordinates. Kinda disappointing, considering some of the questions in the text would me much easier to solve in spherical, rather than converting everything to Cartesian.

In the second edition of Boas, this is the subject of a problem in the section Vector Operators in Orthogonal Curvilinear Coordinates.

 

[omephy]

I vote for Advanced Engineering Mathematics by Allan Jeffrey. And also for the book of the same name by Greenberg.
These books are clear and readily accessible.

 

[javaman1989]

I am taking a class called "Math Methods" this semester in my undergrad physics program. The course description is essentially what the original poster stated their course was on. We are using the Weber and Arfken book talked about in this forum topic.

I have taken Calc I-IV (on a quarter system) and differential equations; and I have never had serious trouble with math. In this math methods course though, I am having a lot of trouble; and I am not grasping the concepts. In class, the professor only has time to explain part of the concept we are learning; therefore, I am relegated to learning most of the concept from Weber and Arfken. For me though, Weber and Arfken explain concepts too abstractly and fast. I understand concepts best when every detail of a concept is discussed; and for me, Weber and Arfken glaze over certain details to jump to what they are proving in a section.

Has anyone else who has read Weber and Arfken felt similarly concerning their treatment; and if so, what did you do to understand the concepts? Also, is there a "math methods" book someone could recommend that treats topics in a more detailed manner than Weber and Arfken?

Sorry for the long post; but I just didn't want to say something like, "I don't like Weber and Arfken's treatment, help me."
Vance

 

[Jorriss]

I am taking a class called "Math Methods" this semester in my undergrad physics program. The course description is essentially what the original poster stated their course was on. We are using the Weber and Arfken book talked about in this forum topic.

I have taken Calc I-IV (on a quarter system) and differential equations; and I have never had serious trouble with math. In this math methods course though, I am having a lot of trouble; and I am not grasping the concepts. In class, the professor only has time to explain part of the concept we are learning; therefore, I am relegated to learning most of the concept from Weber and Arfken. For me though, Weber and Arfken explain concepts too abstractly and fast. I understand concepts best when every detail of a concept is discussed; and for me, Weber and Arfken glaze over certain details to jump to what they are proving in a section.

Has anyone else who has read Weber and Arfken felt similarly concerning their treatment; and if so, what did you do to understand the concepts? Also, is there a "math methods" book someone could recommend that treats topics in a more detailed manner than Weber and Arfken?

Sorry for the long post; but I just didn't want to say something like, "I don't like Weber and Arfken's treatment, help me."
Vance

I felt the same way about Arfken and Weber. A/W is a textbook so it's meant to teach new material, but it is quite a large level above lower division calculus and it leaves a lot out. You won't learn, say, complex analysis from A/W, you'll just learn some methods used in physics.

So, some books which may help to clarify gaps:

For Complex Analysis, Brown and Churchill.

For PDE's and Greens functions, I like Hassani's presentation a lot, or maybe even check out a book like Riley (Mathematical methods) for a brief intro to Green's functions.

For Fourier Analysis and Boundary Value Problems. I don't know any great books first hand but Strauss, Partial differential equations has a chapter on it which may be helpful. And I hear very good things about Brown and Churchill, Fourier Series and Boundary Value Problems.

If you want one single book that will help out, Boas or Riley are good undergraduate mathematical methods books but they definitely will not have everything you will need if you are using A/W.

 

[javaman1989]

Wow! Thank-you for all those suggestions, and I will look into getting those books when we reach those topics.

Also, I didn't earlier note that the class is not going to cover the entire Weber and Arfken book, just some sections; therefore, any book that gives a more detailed treatment of some topic in Weber and Arken would be helpful.

 

[javaman1989]

As a follow up for those that may come across this thread, I borrowed the Riley book from a college library, and it saved me in the class. Thanks to the Riley book, I got an A in the class.
Riley is thorough and explains everything leaving no detail vague.
To be clear, the book I used was: Mathematical Methods for Physics and Engineering by Riley, Hobson, and Bence
ISBN-10: 0521679710

 

[dextercioby]

I particularly like old books, which have the taste of encyclopedia in them and are very well written: Courant & Hilbert, Whittaker and Watson and especially Morse and Feschbach. Surely, they are not published anymore, but they're definitely a better option than the terse and tedious books written today, at least for me.

 

[kaustav saha]

H.C DASS AND VERMA's mathematical physics is also gd 1

 

[theoristo]

These have good review and are cheap :https://www.amazon.com/dp/0486691934/?tag=pfamazon01-20
https://www.amazon.com/dp/0486652270/?tag=pfamazon01-20
https://www.amazon.com/dp/0486600564/?tag=pfamazon01-20

 

[Joker93]

So I managed to borrow a copy of Arfken, and I shelled out the money for the Hassani. I've worked from both now, and I'm not really a fan of Afrken. I will admit, his book is definitely geared towards the notation that was taught in 1st and 2nd year mathematics, and there are a few more examples, and a few less theorems, and proofs etc. But Hassani is actually a pleasure to read. It has well written bio's of different great scientists relevant to that topic (i.e. Green's Functions --> bio about Green)

Further, at this level of physics, we've encountered Dirac's bra-ket notation of vectors in QM, as well as some of the more formal useful notations used in this book. Why delay the inevitable? The newer notations used in this book, are used because they are more powerful then the old notations. Eventually we're going to need to know this stuff. The mathematics is the same behind it, it's really just a matter of wrapping your head around the formalism.

So go Hassani!

Does hassani also provide proofs for the mathematics that he use in his book?