Students examine the foundational components of limits, derivatives, integrals, and series and apply this knowledge to problems in economics and physics. Derivatives are used to find lines tangent to curves and integrals. Students learn specific rules of differentiation and explore real-world applications including related rates and optimization. Students explore the graphs of functions and their first and second derivatives to determine relationships. Functions increase in complexity to include logarithmic and exponential components. Various methods of finding the area under a curve are examined and applied, and each method is supported graphically. Integration is used to revolve solids about an axis. The course ends with an exploration of series and parametric and polar scenarios. Students relate these concepts to problems in other disciplines. At the conclusion of the course, students are able to apply their knowledge to physics problems related to speed, velocity, acceleration, and jerk, and find the volume of an object with curved sides, such as a barrel.
Also available to students is a 45-lesson course designed to prepare them for advanced standardized assessments in calculus. Units 1 and 2 provide a review of derivatives and a number of application problems. Students take the first and second derivatives of functions and work with graphs, examining domain, range, extrema, and concavity as they relate to differentiation. Students look at different types of limits. As they review integration, students find areas under curves, areas between curves, and volumes of solids, and apply integration to physics problems. Unit 3 examines integration by parts, partial fractions, and improper integrals. Students also complete problems working with polar coordinates. The end of this course focuses on specific series and sequences as they relate to previously learned calculus concepts.