From the course: Complete Guide to Differential Equations Foundations for Data Science

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Diffusion equation

Diffusion equation

From the course: Complete Guide to Differential Equations Foundations for Data Science

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Diffusion equation

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- [Instructor] Let's start using the separation of variables technique with the diffusion equation, also known as the heat equation. The goal of this video is to provide you a general understanding of a one-dimensional diffusion equation, but note that you can explore other dimensions of the diffusion equation on your own. Let's start off with the definition. The diffusion equation, also known as the heat equation, is a second-order partial differential equation. This equation is parabolic, meaning it satisfies certain conditions with its constants and corresponding eigenvalues that cause it to have the highest order derivative with respect to time only show up once. This equation describes how the diffusion of some quantity, such as heat, evolves over time. For example, it can analyze how heat flows from a hotter portion of a rod to a cooler portion with the rate of the heat transfer proportional to the temperature gradient. The following is the diffusion or heat equation. So you…

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