# Supplement to spivak's calc on manifolds

• trancefishy
In summary, the speaker has checked out Spivak's calculus on manifolds to work on during their summer in Colorado. They have already completed calc3, matrix theory, and linear algebra, and are wondering if they are ready to tackle the book. They mention having never seen the book before, but believe they should be able to handle it. They also mention that their course recommended looking at Munkres' "Analysis on Manifolds" as well. The only technical prerequisite for Spivak's book is linear algebra, logic, and one variable calculus.
trancefishy
so i checked out Spivak's calculus on manifolds today, to work on while I'm in colorado this summer. i just finished up this semester with calc3 (multivariable), and I've take matrix theory and linear algebra as well. should I be good to go on this book at this point? I'd like to know since I'm leaving tomorrow morning, and therefore lose my access to the university library.

i have never seen that book but generally I think if you're comfortable (ie seen it before) with the stuff in the first chapter or 2 it would be 'safe' to try to work on it.

yeah, right after i posted that, i started up at the beginning. i think I'm good to give it a go, but, it looks like it's going to be a bit tough.

In my course, they suggested that we look at Munkres' "Analysis on Manifolds" as well (whereas Spivak's book was the main book).

the only technical prerequisite for spivak is linear algebra, and logic, and one variable calc.

## 1. What is the "Supplement to Spivak's Calc on Manifolds"?

The "Supplement to Spivak's Calc on Manifolds" is a resource created by mathematician Michael Spivak to supplement his book "Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus". It includes additional material and exercises to further enhance the understanding of the subject.

## 2. Who is the intended audience for this supplement?

The supplement is intended for advanced undergraduate and graduate students studying mathematics, specifically in the field of differential geometry and calculus on manifolds.

## 3. What topics are covered in the supplement?

The supplement covers topics such as differential forms, integration on manifolds, Stokes' theorem, and exterior calculus. It also includes exercises and solutions for further practice and understanding.

## 4. How is this supplement different from the original book "Calculus on Manifolds"?

The supplement expands upon the material covered in the original book and provides additional exercises and solutions for further practice. It also offers a more rigorous and advanced approach to the subject, making it a valuable resource for students looking to deepen their understanding.

## 5. Is prior knowledge of "Calculus on Manifolds" necessary to use this supplement?

While prior knowledge of "Calculus on Manifolds" is not necessary, it is highly recommended as the supplement builds upon the concepts and material covered in the book. It is recommended for students who have a strong foundation in multivariable calculus and linear algebra.

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