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<h1>๐ Adventures in Calculus and Mechanics</h1>
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Choose an adventure. Start anywhere. Learn how change really works.
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<a href="adventure_1_home.html"><strong>๐ Adventure 1 โ Measuring the World (Calculus & Mechanics Intro)</strong></a><br>
Ready to measure the Earth with a stick? Eratosthenes used one shadow and one angle to find the size of the planet. Youโll use the same idea to see how a tiny local measurement can reveal something enormous.
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<a href="adventure_2_home.html"><strong>๐ Adventure 2 โ The Apple and the Secret of Slope</strong></a><br>
Newtonโs apple leads to a powerful idea: slope at an instant. Youโll zoom in on a second-degree curve and use a tangent line to read change right now.</p>
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<a href="adventure_3_home.html"><strong>๐ Adventure 3 โ Derivative Formulas Through Geometry</strong></a><br>
By growing a square and a cube by a tiny amount <code>dx</code>, you can *see* where <strong>2x</strong> and <strong>3xยฒ</strong> come from.
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<a href="adventure_4_home.html"><strong>๐งฌ Adventure 4 โ Falling Objects</strong></a><br>
What really happens when something falls? Follow gravity through graphs instead of equations, the way Galileo first began to understand motion. Study DiVA Charts: Distance, Velocity, and Accelaration.
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<a href="adventure_5_home.html"><strong>๐ Adventure 5 โ Drag Racing</strong></a><br>
See whathappens in drag races and how is that similar to when something falls. DiVA Charts again can explain the motion!
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<a href="adventure_6_home.html"><strong>๐ Adventure 6 โ Going Fast, Then Slow</strong></a><br>
Why does motion speed upโฆ then slow down? By watching areas grow and change, youโll see how total motion is built from tiny pieces.
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<a href="adventure_7_home.html"><strong>๐ Adventure 7 โ Rockets and Changing Motion</strong></a><br>
When acceleration wonโt stay constant, the rules change mid-flight. Rockets show how calculus handles motion that refuses to stay simple.
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<a href="adventure_8_home.html"><strong>๐งญ Adventure 8 โ DiVA: The Layer That Changed the World</strong></a><br>
Distance, velocity, and acceleration stack together into a single picture. This layered view of motion changed science forever.
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<a href="adventure_9_home.html"><strong>โข๏ธ Adventure 9 โ Exponential Change</strong></a><br>
Some things grow explosively. Others fade away quietly. From radioactive decay to population growth, one special curve explains it all.
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<a href="adventure_10_home.html"><strong>โ๏ธ Adventure 10 โ Exponential Change</strong></a><br>
Some things grow explosively. Others fade away quietly. From radioactive decay to population growth, one special curve explains it all.
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<a href="adventure_11_home.html"><strong>๐ Adventure 11 โ Sneaking Up on a Point</strong></a><br>
What happens if you get closer and closer without touching? Limits appear naturally as a way to understand behavior near a point.
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<a href="adventure_12_home.html"><strong>๐๏ธ Adventure 12 โ Peaks and Valleys</strong></a><br>
Where is the highest point? The lowest? Use slope alone to find best and worst outcomes โ no guessing allowed.
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<a href="adventure_13_home.html"><strong>๐งฑ Adventure 13 โ Drawing Curves from Tables</strong></a><br>
Can numbers alone reveal a curve? First and second differences let you sketch functions before knowing their formulas.
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If you can see patterns and ask โwhy?โ, youโre already doing calculus.
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