For those who are curious, the Calculus Option for the IB Maths (HL) (previously called: Series & Differential Equations ) cover:
- Limits (Weierstrass's delta-epsilon definition, Limit Laws, the Squeeze Thm etc etc)
- Continuity of Functions (essential & removable discontinuity, Intermediate Value Thm)
- Differentiable Functions
- l'Hopital's Rule
- Rolle's Theorem & the Mean Value Theorem
- Riemann Sums
- The Fundamental Theorem of Calculus
- Improper Integrals
- Sequences (bounded sequences, monotone sequences, tests for convergence/divergence, comparison test, sequences as functions, . . .)
- Infinite Series (comparison test, limit comparison test, integral test, p-series, approximation by truncating an infinite series, alternating series and its test for convergence, alternating series estimation theorem, absolute & conditional convergence, absolute convergence theorem, ratio test, power series, radius & interval of convergence, differentiation & integration of power series . . .)
- Taylor & Maclaurin Series(Taylor Polynomials, Taylor's formula for Remainder, Lagrange Form for Error Term , Sum & Products of Series, Binomial Series . . .)
- Differential Equations