2024-2025 Course Flipbook v2 - Flipbook - Page 13
SINGLE VARIABLE CALCULUS
In the world around us, one of the only constants is change. While this statement may
seem oxymoronic, its message is at the heart of the study of Calculus. In Single Variable
Calculus, students explore the nature and applications of change through numerical and
analytical methods. By delving deeper into questions related to the nature of variation,
students synthesize their previously-developed
analytical skills in order to discover and use the
rules of Calculus. The class studies limits as a
means to prove derivative functions. Through the
development of a common vocabulary and set of
structures, we use derivatives to analyze curves,
optimize theoretical and practical models, and
relate multiple changing variables to one another
in context. These studies take up a majority of the
year and are focused on instantaneous rates of
change for various functions. Near the end of the
year, the class explores integrals as a means to calculate and understand net change
for non-constant rates. Clear connections in Calculus topics are made with other areas
such as Biology, Physics, and Geometry. Throughout the year, students collaborate to
problem solve and hone their mathematical communications. Ultimately, students use
their new skills in order to create a deeper understanding of how change is modeled in
our everyday lives.
Prerequisite: Analytical Precalculus or department chair approval
MATH SEMINAR: ADVANCED TOPICS
Prerequisite: Single Variable Calculus or department chair approval
MATHEMATICS
Calculus is the culminating math course for many high school students at The
Field School and elsewhere. We know, however, that the 昀椀eld of mathematics
extends vastly beyond the topics that are typically taught in high school. What
does higher-level math look like? How is it used to answer interesting questions
about the world? What kinds of problems are other branches of math being
used to solve? This course is designed to challenge and prepare students who
are interested in these questions and may pursue further study of or careers in
math. Unit topics are focused primarily on additional topics in calculus including
differential equations, volumes of rotation, advanced integration techniques,and
sequences and series, with additional opportunities to learn about number theory,
graph theory, topology, etc. As they work through this material, students develop
their voices as mathematicians, focusing on precision in both written and verbal
communication of mathematical ideas. Excitement, curiosity, and readiness
to explore challenges are encouraged mindsets as students confront rigorous
concepts and problems. In this course, students move between the abstract and
analytical to the concrete, frequently asking, “how can we apply abstract topics to
concrete scenarios?”
