So I'm wanting a solid math book for Christmas. I have a solid background in Calculus and am currently working through baby Rudin. I really want a rigorous book dealing with multivariable calculus and linear algebra. How well does Apostol II do this? Would this be a good continuation book from my current study? If not, what book would you suggest?
EDIT: I really like Apostol's Multivariable Calculus and Linear Algebra book and its format. Will this book accomplish my purpose? Do you think it is a good book?
Best Answer
Ted Shifrin's book Multivariable Mathematics is actually one of the best books of this type while not being very well known. Unfortunately, it's very expensive, so unless you can find it in your library, I would choose something else.
Otherwise I would just recommend Spivak's Calculus on Manifolds together with some linear algebra book. For linear algebra I would recommend either Axler's Linear Algebra Done Right or Linear Algebra by Fiedberg, Insel and Spence