# Calculus

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Category: Mathematics
Slides: 33
Updated: 2026-05-15T22:18:37.554Z
Tags: mathematics, calculus

## Summary

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..

## Slide Outline

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

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