Calculus [Competency Based] (2nd semester)

Course Description

Students examine the foundational components of limits, derivatives, integrals, and series and apply this knowledge to real-world situations. Derivatives are used to find slopes of lines tangent to curves at specified points. 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 reveal the functions’ characteristics. Functions increase in complexity to include logarithmic and exponential components. Integrals are explored as 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. At the conclusion of the course, students learn about series, including Taylor and Maclaurin series, as well as how to prove convergence or divergence using integral and p-series tests.

Course Breakdown

• Riemann sums
• Integrals
• Fundamental theorem of calculus
• Slope fields
• Integration applications
• Areas between curves
• Volumes of rotating solids
• L’Hopital’s rule
• Polar equations and graphs
• Taylor and Maclaurin series
• Convergence tests

Course Goals

1. Apply the rules of integration to find the area under a variety of functions.
2. Solve real-world problems that use exponential change.
3. Identify when to utilize integration by parts using substitution.
4. Apply integration to find the area between functions.
5. Identify the volume under a rotated function.
6. Explain how to construct series.