ADVANCED CALCULUS – MULTIVARIATE
AP CALCULUS BC
In the second half of the fall semester, AP Calculus BC students completed their work on differential calculus and began a study of integral calculus. Antiderivatives and Riemann sums provided a lead-in to the Fundamental Theorems of Calculus which was applied in a variety of physical contexts. The semester concluded with the calculus of exponential and logarithmic functions and we will resume in January with a study of differential equations.
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.
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.
During the first semester, students in Precalculus learned properties of some fundamental functions (linear, polynomial, rational, logarithmic, and exponential functions). They utilized functions as a way to model a variety of real-life phenomena such as modeling earnings of big budget movies, relationships between GDP and life expectancy, and estimating the age of a fetus based on femur length. Second semester will start with an expanded look at trigonometric functions and modeling periodic behavior.
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.
Over the last little while in statistics, students have been learning about probability and probability distributions. They utilized R to calculate probabilities associated with a variety of applications (such as medical testing and airline overbooking). They constructed simulations to learn about the role that random chance plays in statistical inference. As the semester continued, students continually developed their skills in using R as well as applying their model construction skills in a variety of different problems (such as a lab studying the best choice of Halloween candy). Second semester will begin with students diving into statistical inference in great detail along with developing ideas for their Statistics project.
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.