The Geometric Meaning of Differential Equations // Slope Fields, Integral Curves & Isoclines

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What do differential equations look like? We've seen before the analytic side of differential equations, solutions, initial conditions, and so forth. That is, the side involving functions that we differentiate or integrate. In this video we see the geometric side. The geometric version of an ODE is called a slope field or a direction field, and it tells you the slope at any given point. We can sketch these using the method of isoclines which are curves of constant slope. Finally an integral curve is a curve that matches the slope of the slope field and goes through the initial condition.

The geogebra to plot slope fields: https://www.geogebra.org/m/z9c3ndaf

0:00 Intro
1:44 Slope Fields and Isoclines
5:00 Integral Curves
7:35 Analytic vs Geometric Story

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