Interactive visualizations of high-value concepts from UIUC weeder courses. Drag the controls and watch the math change in real time. Each lab teaches one idea; it never produces work you turn in.
Shrink the step h toward zero and watch the secant line become the tangent - the geometric meaning of the derivative.
Drag R and C and watch the capacitor voltage approach the source, with the time constant tau = R*C and the 63.2%-at-t=tau property marked.
See the recursion tree explode exponentially, then watch memoization collapse the repeated subproblems into a linear number of distinct calls.
Raise the equilibrium constant K and watch the A and B mixture re-balance to [A] = C/(1+K) and [B] = C*K/(1+K) for a fixed total amount.
Drag the launch speed and angle and watch the range, peak height, and flight time change - range is symmetric about 45 degrees.
Estimate the exact area under f(x) = x^2 on [0, 3] (area = 9) with n rectangles. Drag the count and the sample point (left, midpoint, right) and watch the estimate close in - the midpoint rule converges fastest.
Drag the mean and standard deviation and watch the bell curve shift and stretch. The shaded band one standard deviation each side always holds about 68% of the area, whatever the mean or spread.
A test comes back positive - what is the chance you actually have the disease? Combine the base rate with the test's accuracy and watch the posterior collapse when the disease is rare, even with a near-perfect test.
UIUC grades more and more of you in the Computer-Based Testing Facility: in person, proctored, no notes, no AI, a hard 50-minute clock. Rehearse a timed practice circuit under those exact constraints - the skill you carry in unaided is the only thing that helps in the room.
These are fixed demonstrations - NOVA's interactive-visual study modality. The frontier work that follows generates a manipulable for the specific misconception in your own course's notation, with the interaction itself as a learning signal.