tl;dr : Is the dependency in the figure attached accurate?
Long Version : I am through with my engineering and am shifting to math for grad school. I am looking forward to re-learning (reviewing) everything (Calculus on wards) that is relevant to me. I have created a rough diagram of what I have to learn, which books I have to refer and the dependency I predict by checking out course prerequisites at Stanford, Princeton, UCLA etc.
I am not entirely new to any of these subjects; there is always a little familiarity but what I want now is mastery. I will be learning by myself.
For Differential Equations, I am thinking of using Simmons and for Numerical Optimization, Nocedal and Boyd for Convex Optimization. Fluid Mechanics is Batchelor. Numerical Analysis I am yet to decide a book on but it could be a Numerical Methods for Engineers type book. Link to the Computational Science Part : Here.
Does this sequence seem OK? Should I do anything differently
Note: I'll be spending about 15 days - a month per subject (which I think will be sufficient since I only have to fill in some holes). All subjects on the same horizontal level, I will working on together.