A highly recommended foundational resource for this topic is the book by Michio Masujima . It is specifically designed to bridge the gap between pure mathematics and physical applications, focusing on integral equations, functional analysis, and the calculus of variations. Core Mathematical Topics
: Solving Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs) is essential for wave propagation, heat conduction, and quantum states. Applied Mathematical Methods in Theoretical Phy...
: Courant, Friedrichs & Lewy (1928) - Established foundations for numerical physical simulations. A highly recommended foundational resource for this topic