ADVANCED CALCULUS – MULTIVARIATE
We studied high dimensional space shapes – lines and surfaces: their equations, associated vectors and tangent line / planes. Application were made to 3D motions (distance/displacement/velocity/acceleration, magnus effect, work in physics), linear approximations (multiple variable interpolation, error analysis) etc.
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.
Propositional logic and predicate logic were explored. We studied mathematical proof methods based on the logic principles. Logic programing (Prolog language) was introduced to make new connections based on given information (part of “artificial intelligence”)
Students in math modeling began the year learning about the math modeling process. How do we actually go about attacking realistic, open-ended, messy problems using the tools of mathematics? Students worked on projects where they utilized MATLAB and some difference equations to model bobcat populations and made recommendations to help stabilize the populations. They also worked on a project where they were trying to find the best place on a college campus to put a coffee stand to maximize profits.
Students have learned how to make ranking systems to be able to determine the best of many possible options, and also how the tools of geometric similarity can be used to model a myriad of different situations (such as how to model the volume of blood pumped by the heart of an animal while running at a constant velocity). Right now, students are diving into empirical modeling and exactly what goes into building a function to fit data.
In PreCalculus this year we began with a basic introduction to functions with an emphasis on transformations of the toolkit functions. This unit was followed with Exponential and Logarithmic functions. Several lab days were spent working on real world applications of linear functions and exponential growth and decay. The students followed up by creating their own real life application problems which they presented to the class.
The year in Statistics began with students working with data visualizations and descriptive statistics. Students learned how to use a statistical software tool called R to construct graphics and calculate statistics. They learned how to appropriately display data in a way that could help them gain insight about a question of interest. Students applied their skills on a project where they generated their own questions and used their statistics toolset to help answer their own questions.
Over the last few students, students have learned about least-squares regression. They learned how to use an extremely powerful tool called multiple regression to help them determine the effects of one variable while controlling for other variables. Right now, students are working on their own projects dealing with linear regression on a number of different topics (such as how GPA and SAT scores are associated with a college’s acceptance rate).