[Math] Introductory book on differential geometry for engineering major

Question

I am an engineering major and looking for a straightforward, easy to understand basic book on differential geometry to get started. At starting point, I am not looking for a comprehensive book (may be Spivak's Comprehensive Introduction to Differential Geometry series). I have background of linear algebra and advanced calculus. I am looking to learn topics such as Lie derivative, covarient-contravarient derivatives, pushforward pullback operations, Riemannian manifolds, moving frames, etc. As I am not from math major, I am confused over many previous questions asking suggestions for differential geometry, such as this, this, this, and many other answers on the similar questions.

From search on good books on the topic, I found out O'neill's Elementary Differential Geometry is meant for first course on the differential geometry. However, as I have very limited knowledge about the differential geometry, I am not sure whether this would be good starting point.

Can someone suggest me a good reference (and prerequisites, if necessary,for studying above topics)? Thanks in Advance.

Answer 1

My 3 favourites are:

• Introduction to Smooth Manifolds - John M. Lee
• Introduction to Manifolds - Loring Wu. Tu
• Analysis on Manifolds - James R. Munkres - expensive and hard to get. I'd recommend for a physicist.

However I am loving:

• Smooth Manifolds - Rajnikant Sinha

And I think that may be better for a physicist. However I've only scanned a Library e-book, my copy will arrive on Monday hopefully.

A great topology book to complement ITSM by JML is:

• Introduction to Topological Manifolds - John M. Lee
• Topology - James R. Munkres
• Introduction to Topology - Gamelin and Greene (nice cheap Dover book, VERY good)
• Introduction to Topology - Bert Mendelson (nice cheap Dover book, VERY good, not as broad as the others but very good none the less)