ADVANCED CALCULUS – MULTIVARIATE
AP CALCULUS BC
AP Calculus students began the year with an investigation of limits and continuity. We then explored the tangent line problem as an introduction to the study of differential calculus. We applied differentiation techniques to a wide variety of functions, learning to represent them analytically and graphically as well as numerically. We also used differential calculus as a tool for solving practical problems in related rates and motion. We are now turning our attention to integral calculus where antiderivatives and Riemann sums will provide a lead-in to the Fundamental Theorems of Calculus.
Students in SVGS Dual Enrollment Calculus are finishing their introduction to differentiation and it’s applications by studying linear motion and its applications to falling bodies and unpacking a car crash. The class recently completed a lab experience where they used the Tracker software (https://physlets.org/tracker/) to calculate the equations of motion for a falling object. The students also recently completed a two week project where they attempted to assign fault in a car accident by using the equations of motion to calculate the changes of acceleration that led up to the accident.
Students in Precalculus have been working with logarithms and exponential functions. They have constructed many exponential/logarithmic models to help gain insight in a variety of contexts, such as:
- Modeling the amount of caffeine in a person’s bloodstream after drinking coffee
- Investigating the logistic growth of an outbreak of Ebola
- Modeled the earnings of movies at the box-office
- Estimated time of death of a victim utilizing temperature readings
The coming weeks will see students expand their toolkit of functions to include polynomial and rational functions.
Students in Statistics have been working with Data Visualization and Modeling. They have been learning R (a statistical environment for statistics computing and graphs) as they construct graphics and create models for data. This month, students have learned about least-squares regression, and have chosen a project to explore the effects that some variables have on another. Students have looked at projects such as:
- The Effects of Poverty and McDonald’s Restaurants on Adult Obesity Rates
- The Relationship between NFL team Red Zone Conversion Rate and 3rd Down Conversion Rate on Wins
They learned about the power of multiple regression and how failing to consider confounding variables (careless use of statistics) can lead to results that deliver an incorrect view of reality.