Calculus Book for Mathematicians: Partial Derivatives and Lagrange Multipliers

[E'lir Kramer]

Hi everyone. I've just gotten through the first 15 chapters of Spivak's Calculus. Though the rest of the book looks fascinating, I'm currently more interested in studying statistical thermodynamics in light of my new-found math knowledge. I am reading through Dill's Molecular Driving Forces, 2nd ed. The book uses partial derivatives and Lagrange multipliers to derive the Boltzmann distribution, which is the fundamental theorem of statistical thermo. Unfortunately, Spivak hasn't covered this in Calculus.

I loved Spivak's style, and the treatment that these two math topics have gotten in the Dill book is criminal. (It's one of those chapters that is just there to give the teacher something off of which to teach. But I don't have a teacher, and I need a better treatment.) Can anyone recommend me a second calculus book written by a mathemetician, for mathemeticians, that includes partial derivatives and Lagrange multipliers?



Mason

 

[MarneMath]

I can't remember if these included Lagrange Multipliers, but two books that met the criteria would be Courant Calculus volume II and or Apostol Volume II.

 

[alissca123]

This is the one you are looking for!
Advanced Calculus of Several Variables by Edwards
https://www.amazon.com/dp/0486683362/?tag=pfamazon01-20

 

[E'lir Kramer]

Thanks all for the suggestions. I'm pleased to see three recommendations for "classics". Since the Courant book is $150, and the Edwards book is $15, I started there. But one day I'd like to add Courant (and Apostol) to my shelf.

 

[mathwonk]

spivak has an excellent short several variables book, calculus on manifolds.

https://www.amazon.com/dp/0805390219/?tag=pfamazon01-20

 

[E'lir Kramer]

Thanks, Wonk. I'd heard that it's a difficult read, but I'll certainly keep it in mind for further studies. I feel like it's hard to go wrong with some of these guys.

MarneMath: Question about Courant: which book exactly?

Methods of Mathematical Physics, Vol. 2 by Richard Courant and D. Hilbert (Jan 4, 1989)
Differential and Integral Calculus, Vol. 2 by Richard Courant, Edward James McShane and Sam Sloan (Jun 13, 2010)

Neither of these books are named Calculus, but the second one is closer.

 

[mathwonk]

it's obviously this one:

http://www.abebooks.com/servlet/SearchResults?an=richard+courant&sts=t&tn=calculus

 

[jbunniii]

FYI, Courant's calculus book was later rewritten as Introduction to Calculus and Analysis. Volume 2 is published in two parts and contains all the multivariable stuff:

Vol. 2, part 1: https://www.amazon.com/dp/3540665692/?tag=pfamazon01-20
Vol. 2, part 2: https://www.amazon.com/dp/3540665706/?tag=pfamazon01-20

You may want to compare these with the earlier Differential and Integral Calculus to see which you prefer.

 

[n10Newton]

There is also a book by Munkres Calculus on Manifolds. Use Apostol vol. 2 & Courant vol. 2 together. Apostol is good but courant is little Rude.