Math 205: Multivariable and Vector Calculus

Learning Goals

This course has been designed to achieve the following learning outcomes by the time you complete the course.

• Foundational Knowledge: You will recognize, understand, and develop intuition for new mathematical concepts rooted in multivariable and vector calculus.

• Connecting Content to Real-World Situations: You will recognize how multivariable and vector calculus arise from real-world problems and contexts, and be able to interpret the real-world implications of their solution.

• Application Skills: You will learn how to create mathematical models involving multivariable and vector calculus that describe a variety of real-world phenomena.

• Teamwork: You will learn how to engage in and facilitate open dialogue with classmates and others about mathematics, in ways that are respectful of differences and establish equitable learning environments.

• Learning How to Learn: You will learn about the latest research on cognitive science and how it can help you become a better student. You will also learn how to pinpoint your areas of academic struggles and develop a plan for resolving them. Finally, you will learn how to become a more independent learner.

Textbook

Though the vast majority of the course's content will come from the lesson notes and videos I've prepared (these are accessible via the Unit links above), some of the practice problems and supplemental material comes from the excellent (and free!) book APEX Calculus 3, Version 4, by Gregory Hartman. You can download the book in its entirety by visiting the link provided.

Syllabus

If you are currently enrolled in this course with me then you've received a copy of the course's syllabus. It details the additional course policies and the course structure. For everyone else, the short story is that this course is structured in a flipped classroom format with a mastery grading scheme for assessments. I wrote about this duo in detail in an article I published in 2020 in a mathematics education journal, but here are the takeaways:

• Students read through the lesson notes and the accompanying videos before class sessions start (you can find these inside the Unit links above).

• They then submit reflections on what they learned, which include questions about summarizing what they learned and about what things, if any, they are still confused on.

• During class sessions I clarify the points of confusion submitted via the reflections and also add additional context and supplementary content, as needed. We then work together on the practice problems in small groups.

• Students are assessed using a mastery grading scheme I call Second Chance Grading. In short, weekly quizzes test for understanding and rather than have midterms, we have Second Chance Assessments. On these assessments, students can re-attempt previous quiz exercises and if they score higher the second time around they receive that new (higher score).

This structure is backed by the latest research on growth mindsets, mastery learning, and the "testing effect." (I discuss all that research in my article on Second Chance Grading.)

Getting Started

If you're ready to get started with the course, click on the Unit 1 link above. That will take you to a preview of the first unit in the course, its goals, and how it connects to the rest of the course. That page will also contain links to the individual lessons comprising the unit. At the bottom of those lesson pages you'll find navigation buttons that will help you advance and go backward between lessons.

I hope you enjoy the course. If you happen to catch any errors or have other feedback, please feel free to email me: ofernand@wellesley.edu.

Oscar E. Fernandez