What are some book suggestions for introductory math and physics topics?

In summary: Real Analysis, Second Edition by Harald Hesse and David P. HesseAdvanced Calculus: Second Edition by David V. WidderDon't know that one.
  • #1
Pseudo Statistic
391
6
Hey,
My friend's about to make an order off Amazon and I thought I'd join in too..

I'm trying to find some decently priced books (preferrably Dover books) on introductory real analysis, electromagnetism, multivariable calculus and vector/tensor analysis (Something preferably including both).

Can anyone make any suggestions for books?

I'm not very experienced when it comes to proofs and set theory and such so I'm trying to find something with a gentle introduction to real analysis.

For the rest, I guess all I can say is that I have firm grounding in single variable calculus and ODEs and can manage the basics in vectors.

I've also had a first year physics course in mechanics and some electricity.

Some books I've found are:

Vectors, Tensors and the Basic Equations of Fluid Mechanics by Rutherford Aris

Elements of Real Analysis by David A. Sprecher

Foundations of Mathematical Analysis by Richard Johnsonbaugh, W.E. Pfaffenberger

Introduction to Analysis by Maxwell Rosenlicht

Advanced Calculus: Second Edition by David V. Widder

Electromagnetism by John C. Slater, Nathaniel H. Frank

Electromagnetic Fields and Waves by Vladimir Rojansky

Electromagnetic Fields and Interactions by Richard Becker


I'd appreciate your feedback on any of these books, or possibly suggestions for others.

Thanks.
 
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  • #2
Another text you might want to look into as a subliment to learning E&M and Vector Calculus is: Div, Grad, Curl, and All That. It's what I used to help me get a better grasp on the usage of vector calc and the authors try very hard to use E&M as their model for dealing discussing vector calculus.

Also, it's a tough read and it isn't really a textbook, but another book to look into that helped me get a better understanding of E&M were Maxwell's: A Treatise on Electricity and Magnetism, both volumes. It was tough to work my way through the first time, but it's the orignal text of Maxwell, and for learning E&M I don't think their is really a better text.

But if you are looking for a textbook on E&M you can't go wrong with:

"Introduction to Electrodynamics"
3rd Edition
By David Griffiths, Prentice Hall

That's all I've got at the moment for E&M and multi/vector calc.

As for anaylsis, I haven't taken a course on it yet, but many of the math majors at my school start out with Advanced Calculus by Fitzpatrick, and they said that they thought it gave them a pretty good book to start with for an introduction to real anaylsis. Another book they used for the Advanced Calculus course was actually called: Intro to Real Anaylsis, but I forgot the author's name, and that might be a better book.

Good luck
 
  • #3
Pseudo Statistic said:
Vectors, Tensors and the Basic Equations of Fluid Mechanics by Rutherford Aris

I like this one. Of course it's the old-fashioned "Tensors are objects that transform as..." approach, but very nicely done. You even get some classical differential geometry of curves and surfaces in the mix.

Foundations of Mathematical Analysis by Richard Johnsonbaugh, W.E. Pfaffenberger

Very nicely organized analysis text.

Advanced Calculus: Second Edition by David V. Widder

Don't know this one, but I do like the other Dover Advanced Calculus by Edwards.

Electromagnetism by John C. Slater, Nathaniel H. Frank
Electromagnetic Fields and Waves by Vladimir Rojansky
Electromagnetic Fields and Interactions by Richard Becker

My favorite of the Dover E&M books is Schwartz, Principles of Electrodynamics, but they have a lot of good ones in this category to browse. Rojansky may be interesting because he seems to be intermediate between, say, Resnick and Halliday and a upper-division E&M text.
 
  • #4
Thanks a lot for the feedback guys!
Keep them coming. :)
 
  • #5
A few more:

Harley Flanders, Differential Forms with Applications to the Physical Sciences

Marvin Chester, Primer of Quantum Mechanics

Introduction to Topology: Second Edition by Theodore W. Gamelin and Robert Everist Greene. Has the hairy ball theorem.

And for fun:

Rudy Rucker, Geometry, Relativity and the Fourth Dimension

George Gamow, Thirty Years that Shook Physics: The Story of Quantum Theory and One, Two, Three, Infinity.
 
  • #6
Oh, and also Fermi's Thermodynamics.
 
  • #7
For tensors, no collection is complete without https://www.amazon.com/dp/0486655822/?tag=pfamazon01-20 was the author of "Ricci Calculus"... the 1954 rewrite of his 1924 version where he draws the first pictures [I have seen] of tensors and differential forms that are found in Misner-Thorne-Wheeler's Gravitation, Burke's Applied Differential Geometry, etc... ) In "Tensor Analysis for Physicists", he actually has photographs of paper models of these differential forms.

What's the big deal? One can actually better appreciate the geometry and physics with a picture of the tensor (as one might do with an arrow to represent a vector). [With a little help from the computer, one can accurately plot these "glyphs" for these tensors.]
 
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  • #8
Foundations of Mathematical Analysis by Richard Johnsonbaugh, W.E. Pfaffenberger

Introduction to Analysis by Maxwell Rosenlicht
Those two are pretty good. For a more advanced one try Real Analysis, Hasser and Sullivan.
 
  • #10
morphism said:
Those two are pretty good. For a more advanced one try Real Analysis, Hasser and Sullivan.
Which would you recommend for a first course in Real Analysis? (Which is more gentle on us math newbies?)

Daverz, would Rojansky be the way to go if my only exposure to electromagnetism has been Halliday/Resnick?

Again, thanks for the comments guys. :)
 
  • #11
Pseudo Statistic said:
Which would you recommend for a first course in Real Analysis? (Which is more gentle on us math newbies?)

you can't go wrong with that pfaffenberger/johnsonbaugh book. first they prove all stuff about limits, functions, etc using the real line (which most are comfortable with), then redo it all for general metric spaces. you find that theorems that are true for functions on the real line are usually true for functions on general metric spaces. there are lots of problems, ranging from verifying that something fits some definition to more involved stuff. & since it's published by dover the price is right too.

i haven't looked at that calculus book by widder much but what little I've seen is good.

that div grad curl & all that book is written by a theoretical physicist so i imagine that it is geared towards people in physics or EE. it seems to be that way anyway; it isn't quite as rigourous as a usual math text. a e&m student would probably get a lot out of it.
 
  • #12
Pseudo Statistic said:
Daverz, would Rojansky be the way to go if my only exposure to electromagnetism has been Halliday/Resnick?

Remember that most of these Dovers are reprints of older books, so you might be able to check them out at the library.

I wouldn't really want to say much about Rojansky without being able to look over the book again. I've only paged through it at Borders (another place you might be able to browse through these books). I do remember that what little vector calc he did use seemed fairly simple. Also, he seemed to include material on Ohm's Law and circuits that you aren't going to get in a more advanced book.

Schwartz is the only of these Dover E&M books I've actually read from cover to cover. I'd put the level at advanced undergraduate. I read his book as we were going through the same material in my Jackson courses. Schwartz was 10 times more readable and understandable. It's really a brilliant book, one of my favorite physics books. He uses the full vector calc approach, so it depends on how your vector calc is, I suppose. He does review vector calc in the first 18 pages, but that's probably too fast if you don't have some experience with it.

A great book at a level between Rojansky and Schwartz is https://www.amazon.com/dp/047187681X/?tag=pfamazon01-20, which has tons of worked out examples, but now we're not talking cheap paperback anymore.
 
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  • #13
Pseudo Statistic said:
Which would you recommend for a first course in Real Analysis? (Which is more gentle on us math newbies?)
Rosenlicht is the easiest of the three. I would say a good sequence is Rosenlicht -> P&J -> H&S. Of course it doesn't hurt to have supplements like Spivak and Rudin.

Also, Widder's Advanced Calculus isn't that good, but that's just my humble opinion.
 
  • #14
Daverz said:
Schwartz is the only of these Dover E&M books I've actually read from cover to cover. I'd put the level at advanced undergraduate. I read his book as we were going through the same material in my Jackson courses. Schwartz was 10 times more readable and understandable. It's really a brilliant book, one of my favorite physics books. He uses the full vector calc approach, so it depends on how your vector calc is, I suppose. He does review vector calc in the first 18 pages, but that's probably too fast if you don't have some experience with it.
So vector calc. would be the main prerequisite for the book? (I'm down with div/grad/curl but atm I'm still trying to get my head around green & stoke's theorems and all..)

I would check a library, but where I am right now there are no English libraries-- atleast, none that I have access to. :)
 

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