TITLE: Differential Equations; A prerequisite to Differential Geometry?
QUESTION [5 upvotes]: Is thorough knowledge in ODEs/PDEs and solution techniques to be considered a prerequisite to the study of Differential Geometry (Specifically Riemannian Geometry)?
If not, how would one describe the relation between the subjects?

REPLY [4 votes]: You need DEs to do differential geometry, like solve geodesic equations, but I do not think you need DEs at all to understand differential geometry. If anything you need differential geometry to understand DEs properly (vector fields on manfolds etc), though you do not really need DG to do DEs. As @janmarqz said the main formal prerequisites for DG is linear algebra & vector calculus (and of course solid background in calculus). A basic grasp of topology does not hurt though. However, I think the most important thing is just mental visualization. It also helps to have texts with good illustrations.