Calculus: The Logic of Change
Like Duolingo, but for Calculus: The Logic of Change. Tomo turns the whole topic into a game you play five minutes a day, until it actually sticks.
For the part of you with thirty open tabs that never became anything.
Free during early access · No credit card · iPhone & Android
Key ideas in Calculus: The Logic of Change
- Algebra calculates change between two separate moments in time
- The slope of a curve is a local property that changes at every coordinate
- Calculus analyzes the continuous flow of motion at a single instant
- A changing slope represents an 'instantaneous speed' that is constantly updating
- Instantaneous change requires looking at the movie of motion, not just snapshots
- Calculus treats curves as a series of infinitely many different slopes
- Distinguishing between static algebraic snapshots and dynamic calculus motion
- Understanding that slope on a curve represents a constantly varying speed
- Average change ignores all the peaks and valleys within an interval
- Calculus reveals the 'true behavior' by zooming into micro-intervals
- Systems can have massive internal activity while showing zero net change
- The 'limit' allows us to observe behavior as an interval shrinks to nothing
- Dividing by zero is mathematically undefined and blocked progress for centuries
- Calculus bypasses the 0/0 wall by calculating what a value 'tends toward'
- Recognizing how average change masks internal system behavior
- Identifying the limit as the solution to the zero-divided-by-zero paradox
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 Logic 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.
Imagine you are hiking a rolling hill. How would you describe the steepness (the slope) of the ground beneath your feet?
Get it right to open this lesson and 23 more in the app.
Where Calculus: The Logic of Change takes you
Move beyond memorizing formulas to understand why calculus is the inevitable language of a moving universe. Discover how the connection between change and accumulation solves the world's most complex problems.
- 1
The Bridge to the Infinitesimal
- Seeing Change as a Constant
- The Limit as a Safety Net
- 2
The Power of Local Truth
- Linearization: The World is Locally Flat
- Optimization: Finding the Peak
- 3
The Symmetry of Accumulation
- Summing the Infinite
- The Fundamental Theorem as a Bridge
- 4
Calculus in the Wild
- Differential Equations: The Language of Growth
- Taylor Series: Building the Complex from the Simple
4 sections · 8 units · 24 levels. Built to play, not to enroll.
You pick the voice
Calculus: The Logic of Change is taught in the The Storyteller style: every lesson is a story. 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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