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LearnMathora

The course

Calculus, one honest idea at a time.

Each lesson takes minutes, not hours. Ideas come as pictures first, plain words second, symbols last — and every lesson hands you to the next.

  1. 01FunctionsBefore calculus can describe change, we need a way to describe relationships. A function is just that: a dependable rule that turns each input into exactly one output.
  2. 02GraphsA graph is a function made visible: every input–output pair becomes a point, and together the points draw the function's whole personality at a glance.
  3. 03Slope & rate of changeSlope is the number that says how fast one thing changes compared to another. It's the single most important number in calculus — everything else is refinements of it.
  4. 04LimitsA limit asks: as the input creeps toward some value, what are the outputs closing in on? It's how mathematics talks precisely about “getting infinitely close” — without ever dividing by zero.
  5. 05DerivativesThe derivative is the slope of a curve at a single point — the instantaneous rate of change. It answers “how fast, right now?” for anything a function can describe.
  6. 06Basic derivative rulesYou could compute every derivative from the limit definition — but you'd grow old doing it. A handful of patterns covers nearly every function you'll meet. Learn the pattern, and the formulas remember themselves.
  7. 07AntiderivativesAn antiderivative runs the derivative backwards: given the rate of change, recover the original quantity. If you know the speed at every moment, can you rebuild the journey? Yes — that's antidifferentiation.
  8. 08Basic antiderivative rulesEvery antiderivative rule is a derivative rule read backwards. Master one reverse move — raise the power, divide by the new power — plus a few special characters, and the essentials are yours.
  9. 09Integrals & areaAn integral adds up infinitely many infinitely small pieces. Geometrically: the area under a curve. Practically: the total accumulated by a changing rate.
  10. 10The fundamental theoremDerivatives measure change; integrals accumulate totals. The fundamental theorem of calculus reveals they are the same operation, run in opposite directions — and turns area problems into two function evaluations.
  11. 11Optimization & related ratesDerivatives don't just describe change — they find best values and connect linked rates. This is where calculus starts paying rent.