M 427L: Vector Calculus
Summer 2025, University of Texas at Austin
Dr. Alex Macedo
We start the course with a discussion of curves and surfaces in \u211d2 and \u211d3. To study those objects, we introduce tools such as matrices, inner products and the cross product.
We then proceed to develop calculus for scalar a vector-valued functions of several variables. In particular, we discuss their limits, derivatives and integrals.
We finish the course with Stokes’s theorem, which relates the integral over the boundary of a curve or surface U \u2282 \u211d3 to the integral of a suitable object over U.