Books for Geometry, Real Analysis and EM

[Devil Moo]

Hi, all.

I would like to read books about the topics - Geometry, Real Analysis and Electricity and Magnetism. And I find the followings. Are they decent and rigorous?

Geometry

The Real Numbers and Real Analysis

Introduction to Electrodynamics
Classical Electricity and Magnetism
Electricity and Magnetism
Classical Electrodynamics

 

[enrev91]

The real analysis text is very good for a first course. It's somewhat unorthodox in its decision to banish sequences and series to the hand. I've finished the first four chapters and so far the book is very clear and easy to follow, and best of all is very rigorous. Everything is proven from first principles: you start with Peano's axioms and make your way up to R, you prove the uniqueness of the real numbers and the viability of their decimal expansion (before you even discuss limits!).

Griffith is good, if you've done well on your multivariable calculus course you'll find it very easy to follow.

I'm using Bloch for self-study and I took a university course using Griffith (and O. N. Sadiku). I can't speak about any of the other books.

 

[Devil Moo]

I once finished the part starting with Peano's axioms. Wow, it is inspiring.

 

[Henga]

Hi, all.

I would like to read books about the topics - Geometry, Real Analysis and Electricity and Magnetism. And I find the followings. Are they decent and rigorous?

Geometry

The Real Numbers and Real Analysis

Introduction to Electrodynamics
Classical Electricity and Magnetism
Electricity and Magnetism
Classical Electrodynamics

I would like to suggest you The Geometry: A Comprehensive Course book.
This amazing geometry course book is for enriching your geometry knowledge
comprehensively. You will get all the important theorem together in this book. Also, You will find the solution to Napoleon's test problem: How to construct the center of a circle using only a compass. In a word, that will be the best book for geometrist mathematicians.

 

[member 587159]

I also read parts of Ethan Block. It is a good book. IThe chapter of derivatives and Riemann-integrals are very enlightening, and mention/prove much more results than most intro real analysis texts.

Another very good book is Spivak's calculus.

 

[BPHH85]

Hi

As a book for the beginning, I liked Elementary Real Analysis a lot. There is also a book from the same authors for graduate students about real analysis. Both books you can buy as a paperback or get them as a slide style pdf version legal and for free here.

EDIT:
For E&M I can recommend Zangwills "Modern Electrodynamics". It's a very good book but you should bring some foundation in E&M. I won't recommend it for the very first contact.

 

[MidgetDwarf]

I would recommend the Bloch book. Very good explanations and interesting way of doing things. I would also buy an old edition of Lay: Introduction to Real Analysis. Very easy book to understand, review of sets, logic, and very small. Read parts of Lay that you may find difficult, then go back to Bloch.

 

[vanhees71]

The E&M books are all pretty good. As an additional reading, I'd strongly recommend to also have a look at Landau and Lifshitz vol. 2. It's starting from the relativistic formulation right away, which is (in my opinion) the best approach since Maxwell's equations are in fact a relativistic classical field theory and thus much simpler when formulated relativistically, but of course to appreciate this, it's good to have some intuitive idea about the subject from the traditional approach of the other books. The only book I really cannot recommend about E&M is Berkeley physics course vol. 2 by Purcell. It's also taking the relativistic view from the very beginning but buries its beauty under a layer of bad didactics. To avoid the appropriate vector and tensor calculus in relativity is making the subject harder rather than easier, and you've to learn it anyway as a mathmatical tool!

 

[CJ2116]

The E&M books are all pretty good. As an additional reading, I'd strongly recommend to also have a look at Landau and Lifshitz vol. 2. It's starting from the relativistic formulation right away, which is (in my opinion) the best approach since Maxwell's equations are in fact a relativistic classical field theory and thus much simpler when formulated relativistically, but of course to appreciate this, it's good to have some intuitive idea about the subject from the traditional approach of the other books. The only book I really cannot recommend about E&M is Berkeley physics course vol. 2 by Purcell. It's also taking the relativistic view from the very beginning but buries its beauty under a layer of bad didactics. To avoid the appropriate vector and tensor calculus in relativity is making the subject harder rather than easier, and you've to learn it anyway as a mathmatical tool!

This is an interesting comment because I've always been flabbergasted by the number of rave reviews/recommendations of Purcell's book. I bought it about 5 years ago and have tried many times to dig into it, but have come up scratching my head on most of his explanations. The one positive I will say is that Morin's update has a lot of really good and non-trivial worked out exercises, which I have referenced from time to time.

I definitely agree with BPHH85's comment on Zangwill's book. I have been working through this, paired with Griffith's, off and on for a few months and can honestly say that this is one of the better textbooks I have ever used. His sections on the Helmholtz theorem and tensors are really well explained (although the Fourier series/transforms not so much..)

 

[vanhees71]

I forgot to mention that there's a much better textbook with a similar approach as Purcell's:

M. Schwartz, Principles of Electrodynamics, Dover (1984)

 

[MidgetDwarf]

I know this thread is old. But for anyone looking for a geometry book, I highly recommend Moise: Elementary Geometry From An Advance Standpoint.