# Multivariable Calc Books: Similar to Spivak's Calculus?

DarrenM
Hello there,

I'm currently enrolled in Calculus II (Integral Calculus), and I am slowly working my way through Spivak's Calculus.

I intend to take Multivariable Calculus next semester. The course description is as follows:
Syllabus said:
This course includes the study of vectors, solid analytical geometry, partial derivatives, multiple integrals, line integrals, and applications.
Course Catalog said:
Real-valued functions of several variables, limits, continuity, differentials, directional derivatives, partial derivatives, chain rule, multiple integrals, applications.

I was wondering if there were any clearly recommended books, similar to Spivak, for the above-mentioned class/content. I've got a couple of calculus textbooks that include multivariable content, but I'm looking for something that takes a more rigorous approach as a supplement.

Also, since I'm here already, I'll be taking a Discrete Mathematics course with the following course description:
Introduction to discrete structures which are applicable to computer science. Topics include number bases, logic, sets, Boolean algebra, and elementary concepts of graph theory.
I would very much appreciate any suggestions in that direction as well. This is the required text https://www.amazon.com/dp/0534359450/?tag=pfamazon01-20.

Sincere thanks for any help.

Last edited by a moderator:

yottzumm
Also, since I'm here already, I'll be taking a Discrete Mathematics course with the following course description:

I would very much appreciate any suggestions in that direction as well. This is the required text https://www.amazon.com/dp/0534359450/?tag=pfamazon01-20.

Sincere thanks for any help.
When I studied Number Theory, back in the 80s, we used the text "An Introduction to the Theory of Numbers" by Niven and Zuckerman https://www.amazon.com/dp/0471625469/?tag=pfamazon01-20 --can you believe it, I still have the book. I can't tell you whether number theory and discrete math are exactly the same thing, but they are certainly related. I fell asleep in that class a lot. Basically, back then number theory had one application: Making soundproof rooms. However it is said that number theory is the queen of mathematics.

Last edited by a moderator:
yottzumm
From my reading of Wikipedia, it looks like Discrete Mathematics covers a lot of ground of which, Number Theory is a small piece which also interacts with Continuous Mathematics. Also I see that number theory has application in cryptography (factoring of large numbers). Do you know what you'll be studying in your class? That might give us a better idea of which books to recommend. Perhaps a better recommendation would be Godel Escher Bach: An Eternal Golden Braidhttp://www.google.com/url?sa=t&sour...o_28BA&usg=AFQjCNF5uApwP33mpSyy7w5YpA5UT2FnBw by Douglas Hofstadter. EDIT: Ignore the book on Number Theory, I just read your quoted section. Definitely get Godel Escher Bach (one of the less expensive books you'll be buying).

Last edited by a moderator:
union68
Well, Spivak's Calculus on Manifolds is the likely suggestion.

However, the theory behind calculus in R^n is usually written in differential forms and a bunch of other fancy math. This is how the aforementioned book is, how Munkres' Analysis on Manifolds is, how chapters 9 & 10 in baby Rudin are, etc.

They'll cover the same thing as your calc III class will, but in a very different way.