Calculus for the IB and the APs

Course Description:

This will be a very extensive course covering all of the IB AA HL calculus and most of the AP Calculus BC portion and more. The topics the course will cover are:

- Limits: Solving for limits, Squeeze theorem, Intermediate Value theorem, Connecting limits to asymptotes.

- Differentiation: Rules of differentiation, Product, Quotient and Chain rule, Inverse functions, Trigonometric and Inverse trigonometric functions, Logarithmic diffrentiation, Parametric equations, Implicit Differentiation, Related Rates, Optimisation, Mean Value theorem, Extreme Value Theorem, Kinematics, L'Hopitale's Rule.

- Integration: Rules of integration, Riemann Sums, Integration by substitution, Integration by Parts, Integration by Partial Fractions, Kinematics, Area between curves, Volumes of cross-sections, Volume around the axes, Arc length.

- Differential equations: Slope fields, Euler's method, Solving first-order differential equations using separation of variables, substitution and integrating factor, Solving second order differential equations, Logistic models

- Series: Taylor and Maclaurin series

Note: A previous knowledge of functions and trigonometry is required.

Frequency of the course: 3 classes per week

Duration of a class: 1.5 hours