Courant & John's Introduction to Calculus and Analysis

[devious_]

Does anyone know how many chapters Courant & John's "Introduction to Calculus and Analysis, Volume II" has? Because I've found a 4 chapter reprint, and was wondering if I should get it.

 

[devious_]

Nevermind... I think I understand now: there are two parts to the second volume, and this happens to be the first one.

 

[MathematicalPhysicist]

the new ones of springer are of total of 3 volumes (including the first volume), while the first editions are only 2 books.
but quite hefty, and with applications to physics.

 

[devious_]

Indeed. I saw the second volume at my school's library the other day. It was huge.

I own the first volume and, having read through large chunks of it, find it an excellent text. So I decided to see if the same applies to the second volume.

 

[mathwonk]

if you read those 2 volumes, no one will know more calculus than you.

 

[duke_nemmerle]

if you read those 2 volumes, no one will know more calculus than you.

Wow, Mathwonk seems to be really pleased with Courant. So much so that I'm contemplating picking up the two volumes. I've found Stewart's book to be a breeze for the most part(self-teaching). Perhaps I should look into something more detailed and rigorous?

What is it about Courant's book that impresses you most, if you don't mind my asking? Is it the rigor? The depth? I'd be really interested in knowing.

 

[t!m]

if you read those 2 volumes, no one will know more calculus than you.

Not even Richard Courant.

 

[devious_]

What is it about Courant's book that impresses you most, if you don't mind my asking? Is it the rigor? The depth? I'd be really interested in knowing.

Courant is amazing. I promise you that you can find anything related to calculus (be it application or theory) in that text.

I just simply love his approach. He doesn't use the usually dry definition-theorem-corollary approach, but instead he actually motivates everything and gives proofs that feel so intuitive you can't help but feel they're actually informal. Sometimes the more technical proofs (along with other interesting examples, applications, etc.) are left in the appendices so as to not hinder your first attempt at understanding the material. Plus the exercises are just fantastic! You can find a lot of difficult problems in there (even ones that appear in Spivak).

I actually picked up the first volume after mathwonk recommended it. At first I didn't like it all that much, but now it's grown on me. Personally I recommend the "Courant & John" version as opposed to the vanilla "Courant" one. I don't know why, but I liked the structure of the former more.

 

[MathematicalPhysicist]

devious, when you mean vanilla one, do you refer to the volumes entitled:"differential & integral calculus"?

 

[devious_]

Yes, those. I read "Introduction to Calculus and Analysis".