Ok thhe follwoing questio is extremely silly. everything else that I've read in the book makes sense but this part doesn't. i just can't seem to udnerstand it because of a combination of stupidity and notation. Near the end of page 69 an identity is derived to show how the components of the gradients transform. That made perfect sense. He then shows us the new notation for partial derivatives and suddenly jumps to showing us what the basis of the gradient one form is. This didn't really make sense to me. firstly could you expand the sumbol and shoe me exactly what it means? Secondly could you show me why that's the basis for the gradient one form? Please exaplain EVERY step. I just can't seem to understand it. The book assumes that you're moderately smart which I'm not. This is of course directed towards those who have the book. If you don't have it the part I don't get is on this page. http://www.mth.uct.ac.za/omei/gr/chap3/frame3.html I have absolutely no idea how we get from 23 to 24. what does dx^alpha mean? And please don't start barraging me with questions just because i'm in highschool. I really didn't like it. Yes I do know multivariable, i do know some linear algebra and I do know something about differential equations. THis is a first course in general relativity.