>>11598552>DEsTenenbaum for computational ODE.
Strogatz Nonlinear Dynamics and Chaos for theoretical ODE (a second course).
Strauss for computational PDE + some theory.
Evans for the full PDE theory.
>Discrete mathI thought Rosen was quite good, though others dislike it.
>Functional analysis, complex analysisStein and Shakarchi. Should be them for Fourier as well, and even maybe for Real.
>Differential geometryDo Carmo for diff geo of curves and surfaces.
Spivak calculus on manifolds for manifolds, differential forms, etc.
Guillemin and pollack for diff top.
Lee Smooth manifolds/riemannian geometry for the real deal.
>Algebraic topologyThe common sentiment is "read hatcher until you realize it's shit, then you're ready to switch to fuchs-fomenko."
>measure theoryI recommend Stein and Shakarchi real analysis but there are other good options.
