Customer Reviews

Multivariate Calculus and Geometry (Springer Undergraduate Mathematics Series)

5 star:		(0)
4 star:		(1)
3 star:		(0)
2 star:		(1)
1 star:		(0)

 

 

This is not an elementary textbook, it is in fact aimed at higher level undergraduates. This means you shouldn't be afraid of theorems & their proofs, you should know some linear algebra, including some familiarity with n-dimensional euclidean space, as well as partial derivatives and elementary calculus. The author's Functions Of Two Variables could be profitably read before tackling the present book.

The book is about the differential and integral calculus of multivariable functions, including a very nice introduction to the classical elementary diffential geometry of curves & surfaces. A bent on differential geometry can be perceived all along.

The style is elegant and crisp and rather intuitive. All in all it is a very nice book. I didn't give it five stars because some of the stuff you'd expect to find in an advanced calculus book, such as series (including Taylor's series) and a careful discussion of differentiability, are missing.(This review is about the first 1998 edition).

But not for someone who wants to learn at his own pace.
It starts with the Matricial definition of derivatives and assumes
a complete knowledge of Matrix Theory.

This, at least for me, is neither intuitively nor psychologically
friendly. Other math books, which are not even targetted at
undergraduates are easier and more fun to follow
(e.g. Algebra by B.L. van der Waerden Algebra: Volume I)

Boring, maybe good for someone at college who has a teacher and
need to pass an exam.

If you are a math nerd who can follow books like:

Theorem
Proof
Corollary
Proposition
Proof
Corollary
Proposition
Lemma
Proof
Corollary
Theorem
Proof
Corollary
...
[Some Explanatory Text]
...
Theorem
Proof
Corollary
Proposition
Proof
Corollary
Proposition
Lemma
Proof
...
[Figure]
...

Then this is the book for you.