I'm pretty interested in study partial differential equations applied, in my undergraduate I take a introductory course in PDE and now I'm going to applied to master in applied mathematics so my questions is what textbook you reccomend me for study PDE Applied to real world.
Also I'm focus in optimization theory (My project degree was about local and global extrema).
Partial Differential Equations for Scientists and Engineers by Stanley Farlow. This is for learning PDE.
For solving PDEs, go for FENICS, which is a python software for solving PDEs using finite element analysis. There are many good book recommendations for FENICS on the fenics website.