Calculus: The Mathematics of Change
Bridge the gap between algebra and higher mathematics by mastering the logic of limits, derivatives, and integrals. This course prepares you for the rigors of College Calculus II by focusing on the 'why' behind the formulas.
Like Duolingo, but for Calculus: The Mathematics of Change. Tomo turns the whole topic into a game you play five minutes a day, until it actually sticks.
24 levels across 4 sections, about 48 minutes end to end, roughly 10 days at five minutes a day. It moves through The Language of Change, The Power of the Derivative, Accumulation and Area, and Advanced Techniques and Series. It assumes you already know the basics.
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Key ideas in Calculus: The Mathematics of Change
- Continuous domains allow for any value within an interval
- The inner function must be evaluated first
- Discrete ranges restrict outputs to specific values
- Function composition is non-commutative
- Calculus models transition from discrete to continuous
- Output of first process becomes domain for second
- Distinguishing between continuous input domains and discrete output sets
- The sequential logic of function composition
- Inverse functions undo operations
- Vertical asymptotes and undefined fractions
- Continuous vs discrete domains
- Inverse graph reflection
- Asymptote magnitude
- Function composition logic
- Behavior at discontinuities
- Exponential growth rates are proportional to the current value, not a fixed amount.
You've tried the other tabs
Thirty open tabs. Four facts you actually kept.
You watched. You nodded. By Sunday it was gone.
One answer, then back to scrolling.
Eight weeks. You meant to finish. You didn't.
Tomo gives Calculus: The Mathematics of Change the Duolingo treatment: levels, streaks, and quick quizzes that test what you just learned. That game loop is what the tabs above never had, so it's the one you actually finish.
Here's what playing it feels like
A real question from this course. Take your best guess.
When you put one function inside another, which part of the system needs to do its work first?
Get it right to open this lesson and 23 more in the app.
How to learn Calculus: The Mathematics of Change, step by step
Go in order. 24 short levels across 4 sections, about 48 minutes in all, five minutes a day.
- 1
The Language of Change
- Functions as Dynamic Systems
- The Limit: Approaching the Impossible
- 2
The Power of the Derivative
- Instantaneous Motion
- Optimization and Curvature
- 3
Accumulation and Area
- Summing the Infinitesimal
- The Fundamental Connection
- 4
Advanced Techniques and Series
- Integration Strategies for Calculus II
- Infinite Series and Convergence
4 sections · 8 units · 24 levels. Built to play, not to enroll.
Questions about Calculus: The Mathematics of Change
How do I learn Calculus: The Mathematics of Change?
Go in order: start with The Language of Change, then The Power of the Derivative, then Accumulation and Area, then Advanced Techniques and Series. On Tomo that's 24 short levels, about 48 minutes in all, played five minutes a day. Start free and play the first level in under a minute.
Is there a Duolingo-style app for Calculus: The Mathematics of Change?
Yes. Tomo works like Duolingo: short daily lessons, streaks and quick quizzes. Calculus: The Mathematics of Change is one of its free courses, and you can type any other topic to get a course of your own.
Is the Calculus: The Mathematics of Change course free?
Yes. Calculus: The Mathematics of Change is playable on Tomo's free plan, which doesn't expire. No credit card, no waitlist. Download the app and start your first lesson.
How long does it take to learn Calculus: The Mathematics of Change?
24 levels across 4 sections, about 48 minutes of play in total. It's built for five minutes a day, so you finish it a little at a time instead of all at once.
Do I need any background to start Calculus: The Mathematics of Change?
No. It's pitched at an intermediate level, so it starts where you are and builds up. If you can tap a phone, you can start.
Tomo is in ChatGPT
Tomo is also a ChatGPT plugin: the same playable courses, built and played inside your chat.
Add Tomo to ChatGPT- What to ask
- “Make me a Tomo course on black holes.” “Turn this chat into a Tomo course.”
- What you get
- Quick questions with instant feedback, hearts and stars, ready to play in about a minute.
- Where it goes
- No sign-up to start. Connect your Tomo account and your streak carries on in the app.
You pick the voice
Calculus: The Mathematics of Change is taught in the Explain Like I'm 5 style: no big words. promise.. Want a different feel? In the app you can spin up the same topic in any of Tomo's teaching styles. Same facts, totally different vibe.
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Start Calculus: The Mathematics of Change today.
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