Supplement for spivak's calculus on manifolds

[sam90]

im trying to read calculus on manifolds by michael spivak and am having a tough time with it. if anyone could recommend a more accessible book (perhaps one with solved problems) id really appreciate it.

 

[transphenomen]

Vector Calculus, Linear Algebra, and Differential Forms by Hubbard and Hubbard has the same material as Spivak yet and starts earlier with linear algebra, set theory, logic, and ends with the Generalized Stokes Theorem. It is also about 5 times longer, is a lot slower in creating the foundations you need and has many problems with the odd ones solved in a solutions manual. Both can be found at http://matrixeditions.com/UnifiedApproach4th.html, yet the book it twice as expensive as Spivaks book and the solutions manual is about another 50% added. All in all, it is not really a supplement as a replacement

 

[Goldbeetle]

I particularly like "Differential forms" by Weintraub. It focuses on differential forms and the vector calculus theorems and objects that they generalize.

 

[xristy]

Two that have been helpful for me are Edwards, "Advanced Calculus - A Differential Forms Approach" with solutions; and Munkres, "Analysis on Manifolds" no solutions and mentions Spivak's text as an inspiration.

 

[osnarf]

http://www.ms.uky.edu/~ken/ma570

I recommend really really trying a problem before resorting to it, but these are the worked out solutions to Spivak's Calc on Manifolds. If I have to use it what I try to do is just look at the first sentence to get a starting point, and then go back to try to solving it. But calculus on manifolds is a great book, if you are at a university go to the office hours of a professor that is teaching calculus that semester and ask if they would be willing to help you. I found a prof who was always willing to answer questions as long as I came in office hours, and that helped a lot.

I more use the above to go and see alternate solutions once I've finished the problem set.

 

[Ashuron]

osnarf

I have always interested to tackle these 3 books..
what do you think is a good preparation before reading them?

I have checked Advanced Calculus - A Differential Forms Approach, and it seems quite readable

I did calc 1-3 + linear algebra + ODE

 

[osnarf]

I can't speak for the book you've mentioned, for calculus on manifolds a rigorous single variable calc book,(spivak, apostol, etc) would probably be necessary if your class was the standard calc class with not much emphasis on proofs, least upper bounds, etc. You should be good on linear algebra as long as you understood your course well.