Recommending books for Diff. Geometry

[Pazzo]

I was wondering if anyone could recommend some books for studying topics such as abstract manifolds, differential forms on manifolds, integration of differential forms, stoke's thm, dRham chomology, Hodge star operator. Our text is A Comprehensive Introduction to Differential Geometry by Spivak. But I think this book is very difficult for a beginner to learn... Thanks in advance

 

[SolsticeFire]

How about this: https://www.amazon.com/dp/0821839888/?tag=pfamazon01-20

SolsticeFire

 

[WannabeNewton]

How about this: https://www.amazon.com/dp/0821839888/?tag=pfamazon01-20

SolsticeFire

That won't cover most of what he wants to learn. This, on the other hand, does cover all you are asking for: https://www.amazon.com/dp/0387954481/?tag=pfamazon01-20

 

[Pazzo]

Thank you very much both! I will go library and compare the two books.

 

[quasar987]

The friendliest introductory book for the stuff you want to learn is

Loring Tu - An Introduction to Manifolds

But it can be "too friendly at time, and so my favorite is still the book recommended by WannabeNewton

 

[Pazzo]

Thank you quasar

 

[micromass]

I was wondering if anyone could recommend some books for studying topics such as abstract manifolds, differential forms on manifolds, integration of differential forms, stoke's thm, dRham chomology, Hodge star operator. Our text is A Comprehensive Introduction to Differential Geometry by Spivak. But I think this book is very difficult for a beginner to learn... Thanks in advance

What do you mean with "beginner"? What differential geometry do you already know? Do you read a book on curves and surfaces?
If you truly know nothing at all about differential geometry, then I fear that even Lee or Tu are not for you. You really need to see the theory in some special cases first before you do abstract manifolds.

 

[lavinia]

I was wondering if anyone could recommend some books for studying topics such as abstract manifolds, differential forms on manifolds, integration of differential forms, stoke's thm, dRham chomology, Hodge star operator. Our text is A Comprehensive Introduction to Differential Geometry by Spivak. But I think this book is very difficult for a beginner to learn... Thanks in advance

Hi Pazzo

For beginning topology, calculus on smooth manifolds, homology theory, and differential geometry of surfaces I passionately recommend the book Lecture Notes on Elementary Topology and Geometry by Singer and Thorpe. This is an undergraduate text designed to teach the modern point of view. The authors are famous research Mathematicians and wonderful writers.

For differential geometry I benefitted from leaning classical geometry of surfaces as well. These books give a wealth of examples that you can visualize and spare you the burden of too much formalism. Struik's book is a classic but somewhat more modern books are Guggenheimer and I think Barrett o'Neil.