Portland Community College | Portland, Oregon

Vector Calculus I is a fun course where we explore the mathematics (and some physics) of objects in our 3D world, including movement (adding time as a fourth dimension). This course is especially important for students with a future in engineering, where developing your skills with modeling objects in our 3D world will be very useful.

Most of the course is about studying functions from ℝⁿ to ℝⁿ (the two "n"s might be different though) and learning about how derivatives and integrals apply to these multi-dimensional functions and what those derivatives correspond to in the physical world. For example a small object moving around in space can be modeled by a function from ℝ to ℝ³. Or the temperature at different places in a room, changing over time, can be modeled using a function from ℝ⁴ to ℝ.

We will frequently use computer tools in class to visualize 3D animations. Your homework will be a combination of (a) an online homework tool where you can practice techniques, find answers, and use the tool to instantly check if you are correct or not, and (b) hand-written (or typed) explanations that allow me to check your deeper understanding of this and that, as well as help you grow your math communication skills.

Most likely we will have three exams, including the final exam during finals week. Some components of each exam might be take-home.

Depending on how many students end up in the class, we might do individual or group projects. With the option to either present them to the class on the last day of class, or turn in a written report of your topic.

Any technology we use will be freely available and run from a web browser.