I am an graduate student interested in fluid dynamics and have almost zero background in differential and algebraic topology. I must say that I do know some analysis (Lebesgue integration plus basics of functional analysis) and some solid linear algebra (including canonical forms etc) plus the rudiments of Abstract Algebra (not including modules or Galois theory). But I don't know any differential or algebraic topology. (i.e I don't know anything about fundamental groups or homology)
However, I need to make a presentation about the Poincare- Hopf theorem in about two months. Is there any reference that contains a fairly elementary discussion of this theorem along with the relevant concepts and perhaps the complete proof which can be followed by someone with no background in these things.
I was told to look at the textbook by Guillemin and Pollack on Differential Topology. Any additional references which are simple and intuitive and present a complete mathematical proof without skipping steps and assuming too much of a mathematical maturity would be gratefully appreciated.