Slope Fields (First-Order Differential Equations)

This ordinary differential equations video explains slope fields, isoclines, autonomous equations, equilibrium points, phase lines, and stability of constant solutions. We begin with what a slope field (or direction field) is and show several examples of what these look like for a first-order differential equation. We show what an isocline is in a slope field--a region of the field with the same slope. We also describe what an autonomous differential equation is, how to find its critical points (or equilibrium points), and how these relate to the constant solutions for the differential equation. We introduce a one-dimensional phase portrait for the slope fields, and show examples of the different types of critical points: asymptotically stable (attractor), unstable (repeller), and semi-stable.
0:00 What is a slope field?
0:56 Example 1
1:40 Example with an isocline
2:30 Autonomous equations and critical points
3:51 Exponential change slope field
4:48 Logistic growth slope field
6:10 Stability of equilibrium points
8:50 Phase portraits

[curtpiazza]

This is COOL! I never saw graphs illustrated like this! I could just imagine the practical applications! ❤