We can calculate the gradient of a tangent to a curve by differentiating. In order to find the equation of a tangent, we: Differentiate the equation of the curve Substitute the \(x\) value into the ...

The study of Lagrangian equations and gradient estimates occupies a critical niche at the intersection of partial differential equations, differential geometry, and variational calculus. Lagrangian ...

The yield spread between long-term and short-term Treasury securities is known to be a good predictor of economic activity, particularly of looming recessions. One way to learn more is through a ...

Elastic flows and gradient flows in planar curves form a vibrant area of research in geometric analysis, where curves evolve in time under rules dictated by an energy functional. Central to this ...