Resource recommendation

Question

Are there more books like Div, Grad, Curl and all that by HM Schey?

It's hard to describe by what I mean by "books like" to someone who hasn't read above mentioned text, but roughly it means teaching the subject from a less rigorous point of view as a first introduction. Being a physics major these books are perfect for me at the level I am currently studying, having said that there are plenty of books that try to do the same but makes it even harder to understand than a proper math text, the likes of which are almost all math methods book for physicists.

Another good point of Schey's book is that it introduces the subject from a physical point of view in a justifiable manner without requiring the understanding of physics discussed in the book beforehand, unlike for example Sadri Hassani's math methods.

The only other book that I find of such manner was Calculus Made Easy by Silvanus P. Thompson.

I don't have any particular topic on which I want recommendations, it could be any topic at any level.

Answer 1

You could try to see this one

Terrance Quinn BASIC INSIGHTS IN VECTOR CALCULUS With a Supplement on Mathematical Understanding

Answer 2

Perhaps a more introductory, yet fantastic resource is the book "Nonlinear Dynamics and Chaos: With Applications To Physics, Biology, Chemistry, And Engineering" by Steven Strogatz.

This book makes the topic so easy, you can read it at bedtime like a novel. Also, the topic is very useful for physicists but is often neglected in physics departments.

Answer 3

"Proofs from the Book" (Aigner, Ziegler) groups particularly elegant proofs in a variety of subjects: number theory, geometry, analysis, combinatorics, graphs. It is an hommage to Paul Erdös: most proofs where chosen by him.

While the book does not pretend to be an introductory text on any subject, in practice it still introduces many interesting pieces of theory, with almost no prerequisite. It can easily be read by an undergraduate. The text is gently flowing, and well illustrated; while addressing non-trivial subjects: quadratic reciprocity law, Hilbert's 3rd problem, Cauchy rigidity theorem, fundamental theorem of Algebra, Sperner antichains theorem, Brouwer fixed point theorem with Sperner lemma...

Answer 4

In physics one sees books and papers with titles like X for Pedestrians, where X is some topic (sometimes mathematical) of interest to physicists. For example, consider Lipkin's Lie Groups for Pedestrians or Madore's Noncommutative Geometry for Pedestrians. The level of presentation of such material varies greatly.

Answer 5

In the realm of "books like", there is one that comes to mind.
A Student’s Guide to Maxwell’s Equations by Daniel Fleisch. It is pretty detailed and at the level of an undergraduate course, but with all the math that you would want. He doesn't deviate from the topic, but the topic covers a lot of ground.