Math
The del operator: grad, div, curl, Laplacian
Connect gradient, divergence, curl and Laplacian with visible fields, a movable probe and independently calculated boundary and area integrals.
Try this
Compare boundary and area integrals computed independently. Click the field to move the probe. Gradient and Laplacian use f = exp(−r²/2); radial and rotational fields have adjustable nonlinearity.
Equations used in the module
Equations grad f = (∂xf, ∂yf); div F = ∂xFx + ∂yFy curl F = ∂xFy − ∂yFx; Δf = div grad f ∮ F·n ds = ∬ div F dA ∮ F·dl = ∬ curl F dA
