This Full PDF is a visual and conceptual introduction to the fundamental ideas and applications of differential equations. It will walk you through the classification of differential equations (like ordinary vs. partial, linearity, order, and homogeneity) using clear definitions and annotated examples. We also talk about the physical meaning of differential equations in modeling dynamic systems, such as oscillations, heat diffusion, and financial instruments like options via the Black-Scholes equation. The PDF takes a look at boundary and initial conditions (Dirichlet, Neumann, Cauchy), solution methods (homogeneous and particular solutions), and the steady-state vs. transient behavior of systems. 

We also present exercises with detailed solutions, so that you can practice everything you learned.

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