Multivariable Calculus & Differential Equations

Girls-Only & ​All-Gender Course; Prerequisite - Completion of AP® Calculus BC or equivalent; 
​Full-year course
COURSE DESCRIPTION
This year-long course covers a typical college-level Calculus III curriculum, including vectors and vector-valued functions, curves and surfaces in space, partial derivatives and gradients, multiple integration, and line and surface integrals. In the course’s final unit, students learn how to identify and solve various kinds of differential equations, including exact first-order equations, second-order homogeneous and nonhomogeneous linear equations, and partial differential equations, and they practice using such equations to model systems from science and engineering. Built on a foundation of sophisticated problem solving, the course also features 3D visualization and model-building activities that help students develop their geometric intuitions about doing calculus in higher dimensions.
WHAT STUDENTS SAY

"I’m learning a lot of new topics that I never thought about. Some of the topics are logical thinking, which is going to help me generally in life because not everything is a math problem where you have to solve for x."

"No matter what school I choose I will have to take multivariable calculus-- thanks to this course, I feel much more prepared to take it in college and feel it will be an easier transition."

"I truly respect and look up to Dr. Braun. I think she's not only an extremely well-versed lecturer but also an empathetic and engaging teacher."

WHAT STUDENTS DO
Learning is an active process at One Schoolhouse. Students design, create and apply. And, they engage with classmates and connect with their teachers through discussions, video conferences, and projects. Specifically, in this class students will:
  • Set goals that drive their learning. Students reflect regularly on their growth, and meet on video chat with their online teacher to review progress towards their goals.
  • Have choice in how they learn new content and practice new skills. Students are given agency to determine the best ways for them to learn.
  • Apply what they are learning to the real world. Learning is meaningful and connects to concepts outside the classroom.
  • Practice constructive engagement in a diverse and changing world. Students interact with classmates from across the country and around the world.
  • Gain academic maturity. Online learning takes greater discipline and independence than a traditional face-to-face classroom. Teachers support students to build this skill.
MEET A TEACHER FOR THIS COURSE
SIGNATURE ACTIVITIES
Examples of signature activities and projects for this course are:
  • 3D modeling: Build a 3D model to illustrate a given description in spherical coordinates.
  • Applet activities: Explore conic sections and quadric surfaces by manipulating 3D visualizations.
  • Video discussions: Collaborate to explore conceptual topics (infinity, graph theory, and others).​
COURSE APPROVAL
This course is approved by the NCAA. 

One Schoolhouse is fully accredited with the Middle States Association of Colleges and Schools and the Western Association of Schools and Colleges through December 1, 2025; we are an approved online publisher for the University of California. 
Carol Braun
Mathematics Teacher
BA & BS Valparaiso University
MS & PhD Northwestern University