Calculus & Probability Lab

Calculus & Probability Lab turns two of the hardest STEM subjects into something you can see, touch, and drag with your finger. Instead of static graphs in a textbook, every derivative, integral, and probability distribution becomes a real 3D object you orbit, zoom, and reshape live.

Whether you're in AP Calculus, a first-year college calculus or statistics course, or just relearning math you forgot, this app trades memorized formulas for visual intuition: drag a point along a curve and watch its tangent-line slope update instantly, or watch a histogram built from real dice tosses close in on the bell curve as you roll.

FUNCTION LAB — 3D VISUALIZER
• 22 function families: lines, parabolas, cubics, quartics, sine/cosine waves, exponentials, natural logs, reciprocals, square roots, Gaussian bumps, logistic S-curves
• Genuine z = f(x, y) surfaces — paraboloids, saddles, Gaussian hills, ripples, sphere caps, cones, tilted planes, monkey saddles, egg-carton surfaces, twin peaks — drag to orbit, pinch to zoom
• Live tangent-line overlay — move a point along any curve and watch the exact derivative f'(x) recompute in real time
• Riemann sum overlay — slide from 1 to 60 rectangles and watch the sum converge to the exact definite integral
• Every formula is closed-form and exact — no approximation, no drift

PROBABILITY LAB — PHYSICS DICE
• Toss physics-simulated dice and build a genuine empirical histogram, roll after roll
• Scenarios span dice-sum outcomes, coin-flip binomial trials, and Poisson arrival processes
• Overlay your empirical results against the exact theoretical distribution on the same chart
• Watch the Central Limit Theorem happen live: enough trials and the histogram closes in on the normal curve
• Track empirical mean against theoretical mean at every roll

LEARNING PATH — 4 WORLDS, ~50 LESSONS
• World 1, Functions & Limits: what a function is, families of functions, slope, one- and two-sided limits, continuity, average vs. instantaneous rate of change, exponentials and logs
• World 2, Derivative Lab: the derivative as slope, power/product/quotient/chain rules, higher derivatives, tangent planes and partial derivatives, critical points, related rates, optimization, the Mean Value Theorem
• World 3, Integral Lab: area under a curve, Riemann sums, the definite integral, antiderivatives, the Fundamental Theorem of Calculus, net change, average value, area between curves, volumes of revolution, improper and numerical integration
• World 4, Probability & Distributions: sample space and events, combining probabilities, the two-dice sum, random variables, expected value, binomial and Poisson models, the normal curve
• Every lesson deep-links straight into the matching 3D lab, so theory and visualization reinforce each other

AI TUTOR
• Tap Explain on any surface, formula, or dice distribution and get a plain-language breakdown of exactly what's in front of you — your specific coefficients, your specific slope, your specific mean and standard deviation, not a generic textbook definition

BUILT FOR REAL STUDY, NOT JUST BROWSING
• Progress tracking across every world and lesson, so you always know where you left off
• A limited number of dice rolls each day on the free tier; upgrade to roll without limits, unlock every function family and 3D surface, every lesson, and the AI tutor
• A clean, dark, distraction-free interface built for a late-night study session, not a cluttered graphing-calculator UI
• Monthly and Annual plans, with a 3-day trial on Annual — cancel anytime in your account settings

Calculus and probability are usually taught as two separate walls of formulas to memorize before an exam. Calculus & Probability Lab treats them as one connected, visual subject — build the intuition once, and the formulas stop needing to be memorized at all.

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