Class Detail

Vectors in n-dimensional Euclidean space. The inner and cross products. The derivative of functions from n-dimensional to m-dimensional Euclidean space is studied as a linear transformation having matrix representation. Paths in 3-dimensions, arc length, vector differential calculus, Taylor's theorem in several variables, extrema of real-valued functions, constrained extrema and Lagrange multipliers, the implicit function theorem, some applications. Students cannot receive credit for this course and MATH 22.

Prerequisite(s): MATH 19B or MATH 20B or AP calculus BC exam score of 4 or 5.

If you completed the prerequisites but get an error message: UCSC Students - Email your proof of prerequisite material to the department at mathadvising@ucsc.edu for approval to enroll.
Newly Admitted UCSC Students - See the next steps at https://summer.ucsc.edu/summer-edge/choosing-classes/summer-math/
Visiting Students - Prerequisite review is waived in the summer. It is in your best interest to take equivalent prerequisite courses.
If this class is a prerequisite for a Session 2 course you want to take, email summer@ucsc.edu for a permission number anytime after you enroll.
From the Instructor: Optional discussion sections with the TAs are TBA. They will be held via Zoom.

Days & Times	Room	Instructor	Meeting Dates
	Online	Staff	06/23/25 - 07/25/25