Mathematics: Applications and Interpretation HL

Advanced calculus and dynamic models

Graph-based calculus, numerical methods, slope fields, phase lines, logistic rates, and constrained optimisation.

Use Newton method iterations Apply one Newton iteration to approximate a root from a starting value. Use fixed point iteration Apply an iteration rule and interpret convergence behaviour. Read derivative information from graphs Use tangent gradient information to interpret instantaneous change from a graph. Use second derivative and concavity Use second derivative information to identify concavity or acceleration. Interpret slope fields Use slope-field information to infer solution direction and approximate behaviour. Model logistic differential equations Use \(dP/dt=kP(1-P/L)\) to calculate a population growth rate. Interpret phase-line stability Use equilibrium and sign information to classify stability in a dynamic model. Optimise with contour constraints Use a constraint and objective structure to identify a constrained optimum.