21-266 Vector Calculus using Matrix Algebra

10 units, Carnegie Mellon University

Vector Calculus using Matrix Algebra is a first course in multivariable calculus for students who have taken 21-241 or equivalent. The course was designed according to the specifications of the School of Computer Science and is recommended for SCS undergraduates; however, it is open to students from all colleges and is synonymous with 21-259 for prerequisites. Topics covered include scalar-valued and vector-valued functions, the principal axis theorem, quadrics (including conic sections and quadric surfaces), new coordinate systems, partial derivatives, tangent planes, the Jacobian matrix, the chain rule, gradient, divergence, curl, the Hessian matrix, linear and quadratic approximation, local and global extrema, Lagrange multipliers, multiple integration, parametrised curves, line integrals, conservative vector fields, parametrised surfaces, surface integrals, Green's theorem, Stokes's theorem and Gauss's theorem. (Three 50 minute lectures, one 50 minute recitation)

Prerequisites: 21-122 and (21-242 (min B) or 21-241 (min B))

Offered: Spring 2027, Spring 2026

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