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This document provides an overview of mathematical methods in physics, including partial differential equations and differential equations. It discusses important second-order partial differential equations like the wave equation, diffusion equation, and Poisson's equation. It also covers general solutions to first and second order differential equations, separation of variables, integral transform methods, and Green's functions. Examples are provided of solving separable, homogeneous, and exact first order differential equations, as well as Bernoulli, Riccati, and other nonlinear equations.