Analysis Where to Purchase Munkres' Analysis on Manifolds" (Hardcover

[bacte2013]

Dear Physics Forum friends,

I am currently trying to purchase Munkres' Analysis on Manifolds to replace the vector-calculus chapters of Rudin-PMA, which is quite unreadable compared to his excellent chapters 1-8. I know that there is a paperback-edition for Munkres, but I heard that the quality (especially the printing and binding) is not great, and the hardcover-edition is much better for the reading and storage. Unfortunately, it seems that the Addison-Wesley stop published the hardcover-edition, and the book is sold in expensive price from other sellers. Is there a way to get a copy of it? If it is not possible, what are some alternatives to Munkres?

 

[micromass]

Spivak's calculus on manifolds is better.

 

[bacte2013]

Spivak's calculus on manifolds is better.

Could you elaborate more about the reasons why Spivak is better than Munkres and Rudin? I was looking for a detailed treatment of the topics including both functions of several variables, vector functions, differentiation, integration, and differential forms.

 

[micromass]

Yep, Spivak covers all of those. Spivak is better than Rudin, because Rudin is pretty much the worst book out there covering this. It also is more theoretical and has better problems than Munkres.

 

[bacte2013]

Yep, Spivak covers all of those. Spivak is better than Rudin, because Rudin is pretty much the worst book out there covering this. It also is more theoretical and has better problems than Munkres.

I see. What is a prerequisite for the Spivak then? I am going to spend a week to review all materials from Chap. 1-8 of Rudin and the linrar algebra of Axler before diving to the calculus on manifolds. Unfortunately, I forgot most (if not all) of materials typical covered on Calculus III...Will that be a serious problem? Also is Spivak's contents basically same as Rudin's Chapters on the vector calculus?

 

[micromass]

You can probably handle it right now. Yes, Spivak covers the same as Rudin, only better.

 

[bacte2013]

You can probably handle it right now. Yes, Spivak covers the same as Rudin, only better.

Thanks! I will purchase the copy of Spivak then. Fortunately, I found an available copy of Munkres at my am library! I will borrow it for the supplement. As for the computational aspects, which book do you recommend for excellent computational problems (including applications to science like physics and biology)?

 

[micromass]

Can you give examples of problems you're looking for?

 

[bacte2013]

Can you give examples of problems you're looking for?

Applications of partial and directional derivatives to the physical problems, relationship between manifolds to electromagnetism, tricky computational problems (a lot challenging than routine problems of Thomas and Lang).

 

[micromass]

Sorry, I can't help you there, it seems like you want a physics book then.

 

[bacte2013]

Sorry, I can't help you there, it seems like you want a physics book then.

It is okay. Since I am going to take Analysis II on the next semester (Rudin), Spivak will fit me the best. Is this also a book which does not do much of a hand-holding? Also does it also explain the multivariable calculus at the Euclidean space too? Please correct me if I am mistaken, but my impression is that the Euclidean and manifolds are quite different from each other.

 

[micromass]

It explains both multivariable calculus on Euclidean space. Then it explains it on manifolds. A manifold is a generalization of the Euclidean space.
You will find no hand holding at all in this book, don't worry.

 

[bacte2013]

It explains both multivariable calculus on Euclidean space. Then it explains it on manifolds. A manifold is a generalization of the Euclidean space.
You will find no hand holding at all in this book, don't worry.

Dear Professor Micromass, have you read a book called "Functions of Several Variables" by W. Fleming? When I purchased Spivak, that book was recommended by people who used Spivak. Can't usually, I would read it from the library, but it is closed now...Is it at the level of Spivak or Munrkes?

 

[mathwonk]

i also find that spivak is available used for about 1/3 to 1/4 the price of munkres (also used):

http://www.abebooks.com/servlet/SearchResults?an=spivak&sts=t&tn=calculus+on+manifolds

 

[mathwonk]

fleming is much longer than spivak (3 times as many pages) and treats lebesgue integration, which spivak does not.

 

[bacte2013]

fleming is much longer than spivak (3 times as many pages) and treats lebesgue integration, which spivak does not.

I purchased Spivak, but I am still deciding whether I should get Munkres, Fleming, or Hubbard since I would like to have thorough treatment of the vector calculus. Plus, I recently got a gift card so I can purchase one of them.

 

[micromass]

I purchased Spivak, but I am still deciding whether I should get Munkres, Fleming, or Hubbard since I would like to have thorough treatment of the vector calculus. Plus, I recently got a gift card so I can purchase one of them.

You know, you probably shouldn't bother with extra books. If you want a thorough treatment of vector calculus, then you should study differential geometry and manifolds.