#calculus

• 16 June 2026 · 6 min

  The Riemann Integral

  Area as a limit of sums squeezed between over and under estimates. Upper and lower sums, the Riemann criterion for integrability, the integrability of continuous functions through uniform continuity, and the fundamental theorem of calculus tying the integral to the derivative.

  • real-analysis
  • integration
  • calculus

• 15 June 2026 · 5 min

  Differentiation and Taylor's Theorem

  The derivative and what the mean value theorem extracts from it. The derivative as a limit, differentiability implying continuity, Fermat's interior-extremum principle, Rolle's theorem and the mean value theorem, and Taylor's theorem with the Lagrange remainder.

  • real-analysis
  • calculus