How to understand differential geometry

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the differential geometry is so abstract to understand. All are terms and theorem. How to understand it? can someone give me some method and guidance to learn it. HELP!!!
 

quasar987

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Yes. Learn the differential geometry of curves and surfaces first!

Some books:

Differential Geometry - Wolfgang Kühnel

Elementary Differential Geometry - Barrett O'Neill

Elementary Differential Geometry - Andrew Pressley
 
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is differential geometry a neccessary tool for physics? I find my space conceptual is bad ><
It do not like calculus gt method to refer and practise. All are conceptual derivative!!!
 

quasar987

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I won't pretend I understood your last post but if you still find elementary differential geometry of curves and surfaces is too abstract, it might be because you do not have the correct geometrical interpretation/intuition for derivatives of maps R^n-->R^m. In this case, you need to read something like

Elementary Classical Analysis - Marsden & Hoffman

Calculus on Manifolds - Spivak
 
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Thanks. This is much more easy to understand. Seems like my basis is not strong enough to proceed to diff geo...
 

mathwonk

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have you looked at the books of david henderson?
 

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