This course previews the development of differential and integral calculus, in preparation for the AP Calculus AB/BC and Calculus section of the IB curriculum offered in the fall. Emphasis is on the fundamentals which form a foundation for understanding calculus, with concentration on the most troublesome aspects for students new to college-level mathematics. Particular topics include, but are not limited to, what follows.
- Informal treatment of limits, including techniques of their evaluation.
- Average and instantaneous rates of change of a function with respect to its argument. Difference quotient and the definition of the derivative. Equation of tangent lines.
- Introduction to differentiation. Power law. Derivatives of polynomial, trigonometric, exponential and logarithmic functions.
- Chain rule for derivatives of composite functions, product rule, and quotient rule. Second and higher order derivatives. Extrema and points of inflection. Graphical interpretation and relations between f, f', and f''.
- Anti-differentiation and introduction to integration. Indefinite integrals of polynomial, trigonometric, and exponential functions. Substitution techniques of integration.
- Area under curves and definite integrals. Introduction to Riemann sums. Applications to kinematics. Introduction to volume integrals.
Classes will be held from 6/7/2021 through 7/28/2021 (16 Total Classes).
Classes will be on Mondays and Wednesdays 4:00PM-6:00PM PST.