Seeking Advanced Text In Mathematics/Mathematical Physics

[Calabi_Yau]

I'm majoring in physics and I'm about to take a course entitled Mathematical Methods of Physics. It covers Sturm-Liouville Theory, Integral Transforms, Fourier Analysis and PDEs.

I read in the thread "So you Want to be a Physicist" that ”Mathematical Methods in the Physical Science” by Mary Boas (Wiley) is good. But by the title of the book, I suspect it is a rather informal and easygoing book. As I am seriously interested in mathematics(I will pursue an academic carreer in mathematics or theoretical physics) and would like a book(probably books since the course deals spans a lot of different topics) that rigorously deals with what I am going to learn.

Books made by mathematicians, and that deal with the subject the way mathematicians deal, so I can really get motivated, I don't like math textbooks that only focus on practical applications.

 

[radium]

I actually have a book called A first course I partial differential equations with complex variables and transform methods by H.F. Weinberger. It is a book written by a mathematician but is also very useful for physicists. I used it quite a bit in my mathematical methods in physics course which covered a lot of the same material your course will be covering. The book is published by Dover so I got a paperback for around $15.

 

[heatengine516]

I've skimmed through the book by Boas and it seems far from informal. I've actually seen it recommended around here as a must-have reference book for physics majors.

 

[Vanadium 50]

I don't see why you can't start with Boas and then move on to something more rigorous.

 

[ModusPwnd]

We had a similar class in undergrad and it was weak sauce. If you want to do math or theory stuff consider taking proper math courses.

 

[NATURE.M]

Mathematical Physics by Hassani may be a good choice then. It covers many topics, in a more rigorous manner than Boas.

 

[SteamKing]

I read in the thread "So you Want to be a Physicist" that ”Mathematical Methods in the Physical Science” by Mary Boas (Wiley) is good. But by the title of the book, I suspect it is a rather informal and easygoing book. As I am seriously interested in mathematics(I will pursue an academic carreer in mathematics or theoretical physics) and would like a book(probably books since the course deals spans a lot of different topics) that rigorously deals with what I am going to learn.

I don't know why you would say that Boas is informal. Now, if the title of the book were ”Mathematical Methods in the Physical Science Coloring Book”, your conclusion would be more justified.

Books made by mathematicians, and that deal with the subject the way mathematicians deal, so I can really get motivated, I don't like math textbooks that only focus on practical applications.

This is a puzzler, too. Physicists generally don't deal with physics as a mathematician would. Have you read no Feynman? I think the approach physicists have is to use mathematics to illustrate and illuminate the physics. You can only get your buzz on by reading dry, abstruse, cryptic mathematical writing? Well, it takes all kinds, I guess, but don't be surprised if you find yourself kind of alone once you start a physics career. There is nothing wrong in being practical.

 

[WannabeNewton]

I don't know why you would say that Boas is informal.

Because it is informal. There's no reason to pretend it isn't as it doesn't diminish the usefulness book in any way.

You can only get your buzz on by reading dry, abstruse, cryptic mathematical writing?

What's wrong with him/her liking books in which math is done properly?

Well, it takes all kinds, I guess, but don't be surprised if you find yourself kind of alone once you start a physics career.

He/she won't be.

 

[Calabi_Yau]

The thing is I am more likely to become a mathematician than a physicist as I have come to realize that for as much as I feel intrigued about physics and their problems, what really drives me is the mathematics and not necessarily the physics. I had suspected this all along, and found that the undergraduate program in physics in my University offered greater flexibility and the possibility of choosing many mathematics courses from the math major program than the other way around. I don't know if I did the right choice, perhaps I never will, but one thing I know for certain is that I want to learn the mathematics I will face throughout the courses the "formal" and "pure" way as a complement to the practical approach I am supposed to be getting and aiming for this course.

 

[ZapperZ]

First of all, I don't understand what is meant by "informal" here. The word gets thrown around as if it has a clear and definite meaning. Do you think all of you here actually are using this word to mean the same thing? Would you all care to tell me what that is?

Secondly, no book in this world is everything to everyone. Surprise! Boas's text has a very specific purpose:

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 courses 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.

In other words, she wants you to be able to USE the mathematics in your physical science courses, but in case you are also inclined, you may also pursue the mathematics further. She had included numerous references that will allow you to do that! But if you are just starting out, how in the world are you going to know all the various different mathematics in physics and engineering that you would need? Think of how many different mathematics classes you will have to take to cover every topic that she covered in the text!

Problem here is that you are trying to use it in ways it wasn't intended to. Use it as a better and more reliable version of Wikipedia. Then if you find something that is intriguing and want to pursue it further, then go dig out some more. But at least you have this convenient location where almost everything you need has been surveyed!

Zz.

 

[Calabi_Yau]

By informal, I meant where the emphasis of the book was put. I will certainly acquire something like Boas for a start, and it seems to have a good reputation here. I will take it into account as well as the recommended books by my teachers.

The reason I asked what I asked here, was because this is a physics forum, where most of the users who have a career in physics had to go through the same type of course in their early years of college, and I was hoping some of you who had the same kind of interest as me, to go further on the topics covered, could advise me on some good books, each one specialized on one of the topics I am going to broadly cover in this course. I think this type of question is best asked on a forum, rather than googled.

I probably won't need such sophistication and understanding to ace the course, this is just a matter of pure interest in the maths behind it. And has nothing to do with whether or not a physicist needs to know such things.

BTW, I guessed Boas' book was informal because it said Physical Sciences, and that includes a whole range of other sciences that don't need much mathematical sophistication :P

 

[ZapperZ]

By informal, I meant where the emphasis of the book was put. I will certainly acquire something like Boas for a start, and it seems to have a good reputation here. I will take it into account as well as the recommended books by my teachers.

The reason I asked what I asked here, was because this is a physics forum, where most of the users who have a career in physics had to go through the same type of course in their early years of college, and I was hoping some of you who had the same kind of interest as me, to go further on the topics covered, could advise me on some good books, each one specialized on one of the topics I am going to broadly cover in this course. I think this type of question is best asked on a forum, rather than googled.

I probably won't need such sophistication and understanding to ace the course, this is just a matter of pure interest in the maths behind it. And has nothing to do with whether or not a physicist needs to know such things.

BTW, I guessed Boas' book was informal because it said Physical Sciences, and that includes a whole range of other sciences that don't need much mathematical sophistication :P

I find that last statement, and what you meant as "informal" to be very puzzling.

Let me emphasize that her book is one of, if not THE, most detailed coverage of the calculus of variation. If you go through the chapter on this topic, then doing Lagrangian/Hamiltonian mechanics in classical mechanics would be a breeze! I would not call such a text as "informal"

Secondly, she called it "physical sciences" to include chemistry and engineering. I would not insult any if thesis fields if I were you by stating that they don't require much mathematical sophistication. It only reveals your ignorance of how "sophisticated" these fields can be.

Zz.

 

[George Jones]

A compromise, authored by a pure mathematician, that covers some of the topics might be "Fourier Analysis and Its Applications" by Gerald Folland,

https://www.amazon.com/dp/0821847902/?tag=pfamazon01-20

From its back cover:

This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern analysis to develop the concepts and reasoning behind the techniques without getting bogged down in the technicalities of rigorous proofs.

 

[micromass]

A compromise, authored by a pure mathematician, that covers some of the topics might be "Fourier Analysis and Its Applications" by Gerald Folland,

https://www.amazon.com/dp/0821847902/?tag=pfamazon01-20

From its back cover:

Excellent and wonderful book! It's rigorous but it does keep the applications in mind. Wonderful primer on the subject.

For Fourier Analysis, the book by Stein and Shakarchi is very good and is intended for pure mathematicians: https://www.amazon.com/dp/069111384X/?tag=pfamazon01-20 If the OP knows measure theory, then I can recommend other stuff.

For PDE, I don't think you can really beat the book by Evans: www.amazon.com/Partial-Differential-Equations-Graduate-Mathematics/dp/0821849743[/URL] However, I don't find it suitable as introduction.

 

[Calabi_Yau]

Thanks a bunch, I will look them up.

 

[kq6up]

This might be what you are looking for:

https://www.amazon.com/dp/0120598760/?tag=pfamazon01-20

I am currently going through Boas and find it perfect for someone who still knows calculus, but has been out of school so long.

I actually came here to make a similar post, so you might want to read the thread I start.

Regards,
Chris Maness