Slope fields make differential equations visible. Learn how to construct and read direction fields, use isoclines, sketch IVP solution curves, distinguish zero-slope curves from equilibria, understand uniqueness, analyze logistic stability, and apply Euler’s method through exact worked examples.
Learn how eigenvalues determine phase portraits in Differential Equations. This Woody Calculus lesson explains stable nodes, unstable nodes, saddle points, spiral sinks, spiral sources, centers, repeated eigenvalues, eigenvectors, and stability.
How can deterministic differential equations create unpredictable behavior? This Woody Calculus lesson explains chaos theory through sensitivity to initial conditions, nonlinear systems, phase portraits, Lyapunov exponents, and the Lorenz attractor.
Eigenvalues and eigenvectors reveal the special directions that unlock Linear Algebra and Differential Equations. In this Woody Calculus visual lesson, learn how Av = λv explains matrix transformations, scaling, diagonalization, matrix powers, solution modes, stability, phase portraits, and why eigenvalues predict long-term behavior in systems before you even solve them.