IB Mathematics Applications & Interpretation Calculus Notes

SL 5.1—Introduction to Limits

SL 5.2—Increasing and decreasing functions

SL 5.3—Introduction to derivatives

SL 5.4—Tangents and normals

SL 5.5—Introduction to integration

SL 5.6—Stationary points, local max and min

SL 5.7—Optimisation

SL 5.8—Trapezoid rule

AHL 5.9—Differentiating standard functions and derivative rules

AHL 5.10—Second derivatives, testing for max and min

AHL 5.11—Indefinite integration, reverse chain, by substitution

AHL 5.12—Areas under a curve onto x or y axis. Volumes of revolution about x and y

AHL 5.13—Kinematic problems

AHL 5.14—Setting up a DE, solve by separating variables

AHL 5.15—Slope fields

AHL 5.16—Eulers method for 1st order DEs

AHL 5.17—Phase portrait

AHL 5.18—Eulers method for 2nd order DEs