Calculus Visual Lab, Interactive Offline Web App for High School Students, Derivatives & Integrals Simulations, Quizzes + PDF Guide EN ES FR
Category: Education / Interactive Tools
Stop memorizing calculus — watch it happen.
Calculus Visual Lab is an interactive offline web app that teaches derivatives and integrals through living simulations. A water tank fills and drains in front of you while the real equation — computed from the numbers you set — updates on screen. Move a slider and the curve, the tangent line, the water level and the formula all change together. Built for high school and first-year college students, AP/IB calculus prep, teachers and self-learners.
It is a single HTML file: open it in any browser (Chrome, Edge, Safari, Firefox) on Windows, Mac, Chromebook or iPad. No installation, no account, no internet needed, no subscription — ever.
▶ WHAT IS INSIDE (10 modules)
• GUIDED LEARNING PATH — 10 short levels from “what is change?” to your own free experiment. Each level has an animation, a control, a formula, an example and a mini challenge. Progress is saved automatically.
• DERIVATIVES — every rule as an experiment: constant, power, constant multiple, sum, difference, product (with the “rectangle picture”), quotient and chain rule (watch the change propagate x → u → y). Exponential, logarithmic, sine, cosine, tangent and inverse trig functions. A slope explorer where you drag the point and see the tangent, plus applications: motion (position → velocity → acceleration), maxima & minima, related rates with a conical tank.
• WATER TANK DERIVATIVE SIMULATION — set inflow, outflow, capacity, initial volume and speed. The status reads RISING / FALLING / CONSTANT exactly when dV/dt = inflow − outflow is positive, negative or zero, and the graphs record V(t) and dV/dt over time.
• INTEGRALS — 13 interactive pages: antiderivative, the constant C, definite integral with Riemann rectangles melting into the smooth area, power rule, linearity, exponential / logarithmic / trigonometric integrals, u-substitution step by step (with equal areas in x-space and u-space), integration by parts and partial fractions (match the curve by adjusting A and B). Integration lab with left / right / midpoint / trapezoid sums up to 500 rectangles, animated.
• WATER TANK INTEGRAL SIMULATION — choose the flow-rate function r(t) (constant, linear, quadratic, sine); the tank integrates it and shows V(t) = V₀ + ∫ r(s) ds with the antiderivative computed symbolically. Area under the flow graph = water in the tank.
• DERIVATIVE ↔ INTEGRAL — the Fundamental Theorem of Calculus in one experiment: drag points to draw the flow rate and watch the tank integrate it, or draw the volume and watch the flow appear as its derivative. Play forward and backward in time.
• EXPERIMENT LAB — build your own experiment: pick a rate-function family or type a custom expression, set the tank, and see r(t), r′(t), V(t), three graphs and a plain-language explanation update instantly.
• 8 REAL-WORLD EXPERIMENTS — water tank, car (speed & distance), population growth (exponential and logistic), cooling coffee (Newton’s law), electricity (power → energy), medicine in the blood (absorption vs elimination, repeated doses), money with continuous interest, and rainfall. Each one answers: what changes? what is the rate? what accumulates? where is the derivative? where is the integral?
• CHALLENGES & QUIZ — 5 topics, 10 questions per round with fresh random numbers: multiple choice, true/false, numeric answers and “which graph is the derivative?”. Instant feedback with explanations, scores saved.
• FORMULA REFERENCE — every formula, searchable; click one to open the matching interactive module.
• Every concept has a Simple explanation and a Mathematical explanation. All formulas are mathematically verified. Interactive graphs: zoom, pan, hover, drag.
▶ 3 LANGUAGES
Switch the whole app — every explanation included — between English, Español and Français from the Settings page.
▶ ALSO INCLUDED: PDF USER GUIDE (19 pages, in English, Spanish and French)
Part 1 is a calculus primer for beginners: change and accumulation, the definition of the derivative, rule tables, derivatives of common functions, integrals and the constant C, the Fundamental Theorem, and worked examples. Part 2 explains every screen of the app with screenshots and tips.
▶ WHAT YOU RECEIVE (instant digital download)
• Calculus-Visual-Lab.html — the complete interactive app (single file, works offline)
• Calculus-Visual-Lab-Guide-en.pdf
• Calculus-Visual-Lab-Guide-es.pdf
• Calculus-Visual-Lab-Guide-fr.pdf
▶ HOW TO USE
1. Download the files after purchase (Etsy sends them to your email / Purchases page).
2. Double-click Calculus-Visual-Lab.html — it opens in your browser.
3. Choose your language in Settings and start with the Learning Path.
Your progress, quiz scores and experiment settings are saved privately in your browser.
▶ GOOD TO KNOW
• Works on desktop, laptop, Chromebook and tablets; phones are supported with a responsive layout (a larger screen is recommended for the graphs).
• Requires a modern browser with JavaScript enabled (all browsers have it on by default).
• This is a digital product — no physical item will be shipped. Because of its nature, digital downloads are non-refundable, but message me with any problem and I will help.
• Personal-use licence: for your own study, your family or your classroom. Redistribution or resale of the files is not permitted.
Questions? Send me a message — I’m happy to help.
© PRINTIVORA