Computational Mathematics
The heat equation is a partial differential equation that describes how heat diffuses through a given region over time. It is a fundamental model in mathematical physics, often represented as $$u_t = abla^2 u$$, where $$u$$ is the temperature, $$t$$ is time, and $$ abla^2$$ is the Laplacian operator. This equation plays a key role in understanding boundary value problems, numerical methods for PDEs, and the classification of various partial differential equations.
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