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Calculus

Calculus is the mathematics of change — of how a quantity behaves as another quantity shifts continuously. It turned the static algebra of equation-solving...

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Calculus is the mathematics of change — of how a quantity behaves as another quantity shifts continuously. It turned the static algebra of equation-solving into a dynamic study of motion, growth, and accumulation. Key sections include: Calcu lus.; Opening What calculus is.; Chapter I Greeks and exhaustion.; Chapter II Kepler's wine barrels.; Chapter III Cavalieri's principle.; Chapter IV Tangent lines.; Chapter V Newton's Principia.; Chapter VI Leibniz and the dx.; Chapter VII The priority dispute.; Chapter VIII Limits made rigorous..

Key sections

  • 01Calcu lus.
  • 02Opening What calculus is.
  • 03Chapter I Greeks and exhaustion.
  • 04Chapter II Kepler's wine barrels.
  • 05Chapter III Cavalieri's principle.
  • 06Chapter IV Tangent lines.
  • 07Chapter V Newton's Principia.
  • 08Chapter VI Leibniz and the dx.

Topics covered

mathematicscalculus

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Slide outline
  1. 01Calcu lus.
  2. 02Opening What calculus is.
  3. 03Chapter I Greeks and exhaustion.
  4. 04Chapter II Kepler's wine barrels.
  5. 05Chapter III Cavalieri's principle.
  6. 06Chapter IV Tangent lines.
  7. 07Chapter V Newton's Principia.
  8. 08Chapter VI Leibniz and the dx.
  9. 09Chapter VII The priority dispute.
  10. 10Chapter VIII Limits made rigorous.
  11. 11Chapter IX The derivative.
  12. 12Chapter X The integral.
  13. 13Chapter XI The fundamental theorem.
  14. 14Chapter XII Differential equations.
  15. 15Chapter XIII Ordinary DEs.
  16. 16Chapter XIV Partial DEs.
  17. 17Chapter XV Multivariable calculus.
  18. 18Chapter XVI Vector calculus.
  19. 19Chapter XVII Stokes's theorem.
  20. 20Chapter XVIII Green's theorem.
  21. 21Chapter XIX Epsilon-delta.
  22. 22Chapter XX Lebesgue integration.
  23. 23Chapter XXI Measure theory.
  24. 24Chapter XXII Stochastic calculus.
  25. 25Chapter XXIII Calculus of variations.
  26. 26Chapter XXIV Calculus on manifolds.
  27. 27Chapter XXV Complex analysis.
  28. 28Chapter XXVI Numerical methods.
  29. 29Chapter XXVII Calculus in physics.
  30. 30Chapter XXVIII Calculus in economics.
  31. 31Chapter XXIX Twenty essentials.
  32. 32Chapter XXX Watch & read.
  33. 33The end of the deck.
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Updated
2026-05-17
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