Advanced Calculus (Anglais) Broché – 21 décembre 2001
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Description du produit
Présentation de l'éditeur
For undergraduate courses in Advanced Calculus and Real Analysis.
This text presents a unified view of calculus in which theory and practice reinforce each other. It covers the theory and applications of derivatives (mostly partial), integrals, (mostly multiple or improper), and infinite series (mostly of functions rather than of numbers), at a deeper level than is found in the standard advanced calculus books.
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Commentaires client les plus utiles sur Amazon.com
The reason I did not give this book five stars is because Dr. Folland's exposition does not really reveal his enthusiasm of this subject, nor does it truly ask the reader to consider the elegance of the subject. Take the example of Section 2.3, the Chain Rule. This section is full of correct and logical facts, as well as some caveat emptor about different notations, but it utterly lacks any appreciation of the chain rule. We get a theorem and that's it. It doesn't even say that "the derivative of a composition is the composition of the derivatives," showing how those two structures commute.
for clarity and precision of the developed concepts and language used .
It is a clear and concise , with pedagogically very conscious choice of topics which allows a very fast access to more challenging texts of Real Analysis.I highly recommend the text for those who want to progress quickly and safely
in Advanced Calculus(Real Analysis).
I 1st encountered multivariable calculus from this book. When I was learning the materials, I found the book neither rigorous nor intuitive. Its readability is extremely low. Its problem comes from its confusion and poor clarity, which is worse than the mathematical maturity requirements.
I would say this is by far the "most difficult" book I have ever read. (For professors considering assigning this book to students: DONT DO IT. I found it a LOT harder to learn from than Spivak's Calculus on Manifolds, Munkre's Analysis on Manifolds. I'm also ok comfortable with big Rudin, but Folland gave me the hardest time in terms of picking up stuffs) Folland presents a little bit of rigorous stuffs here, but only a little. For students who lack the motivation to work hard, they dont know what Folland is doing. For students who smell the incompleteness, it would be such a real pain to supply the proofs and try to develope more complete theories.
As for intuitions, it is very poor too. Vector Calculus by John Hubbard is a great book for intuition (also its approach and rigor). As for problems, Shiffrin's Multivariable Mathematics is much better. In addition, there are free pdfs
Differential Forms: A Geometric Approach, by David Bachman
Manifolds and Differential Forms, by Reyer Sjamaar
That look more advanced but easier to learn from.