Accumulated area
The upper bound of an integral sweeps right, the area under the curve fills in behind it and a gauge along the foot reads the running total.
CSS
Calculus
15 animationsConstrained optimum
Level contours of an objective swell outward until one touches the constraint line in a single point, and the tangency latches.
CSSDerivative plot
A marker sweeps along a curve in the upper panel while the slope it reads is plotted in the panel below, crossing zero under each turning point.
CSSEuler steps
A stepped polyline cuts the corners of the true solution and falls short of it until the step size halves and the walk tucks back against the curve.
CSSGradient descent
A marker steps down a valley curve against the slope, each hop shorter than the last, and stalls on the minimum with its trail behind it.
CSSInflection point
A curvature cup rides an S-curve and flattens to nothing over the inflection mark before opening the other way up.
CSSLimit at a point
Probes run in along the curve from the left and the right toward a point it never takes, while the epsilon band and delta window close onto the limit value.
CSSNewton iteration
A tangent dropped from a point on the curve meets the axis, the next point is read off the curve above it, and three drops close on the root.
CSSPartial sums
Terms of a halving series lay end to end along a rule while the running total creeps toward a marked ceiling it never passes.
CSSPhase portrait
A trajectory spirals inward across a phase plane of direction ticks and comes to rest on the equilibrium point where the axes cross.
CSSRiemann refinement
Rectangles under a curve double in count and halve in width until the staircase closes onto the curve and only the area remains.
CSSSecant to tangent
A chord through two points on a curve pivots as the sliding point closes on the fixed one, resting as the tangent line.
CSSSequence convergence
A marker hops from term to term of an alternating sequence, the overshoots damping as the tolerance band closes on the limit line.
CSSSlope field
A grid of slope ticks holds still while one solution curve threads itself through the field and flattens onto the equilibrium line.
CSSTaylor approximation
One term, three terms, then five: each polynomial hugs more of the target curve before peeling away, with a pip counting the terms.
CSS