CHAPTER 35 / 40
Calculus Foundations: From Zero to Hero
7 lessons · Explore, experiment and understand.
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- Step 143~20m24
What Is a Limit?
Every idea in calculus — derivatives, integrals, all of it — is built on one concept: the limit. Start here, from nothing.
Open lesson - Step 144~20m26⚡Challenge
The Derivative — Definition, Rules, and Practice
The derivative is a limit of slopes. Watch it converge, derive it from scratch, then build every differentiation rule you'll ever need — inc…
Open lesson - Step 145~15m14
Applications of Derivatives
Derivatives aren't just a rule-following exercise — they find the best possible answer to real problems: the biggest area, the smallest cost…
Open lesson - Step 146~15m14
Antiderivatives and the Indefinite Integral
Differentiation and integration are inverse operations. Given f'(x), this lesson finds f(x) — and explains why the answer is never quite uni…
Open lesson - Step 147~10m13
The Definite Integral and Riemann Sums
The area under a curve, computed exactly — by first approximating it with rectangles, then watching the approximation become exact as the re…
Open lesson - Step 148~15m14
The Fundamental Theorem of Calculus
The single most important result in calculus: differentiation and integration are exact inverses of each other. This is also, finally, HOW y…
Open lesson - Step 149~15m14
Integration Techniques — Substitution and Beyond
FTC tells you to find an antiderivative and subtract — but not every antiderivative is obvious by inspection. U-substitution is the workhors…
Open lesson