MATH S-21A Multivariable Calculus

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7-week session | CRN 30189

To see how calculus applies in situations described by more than one variable, we study vectors, lines, planes, and parameterization of curves and surfaces; partial derivatives, directional derivatives, and gradients; optimization and critical point analysis, including the method of Lagrange multipliers; integration over curves, surfaces, and solid regions using Cartesian, polar, cylindrical, and spherical coordinates; vector fields, and line and surface integrals for work and flux; and the divergence and curl of vector fields together with applications.

Course information
Class meetings

Tuesdays, Thursdays, 8:30-11:30 am
Harvard Hall 104

Optional sections to be arranged.

Start date

Tuesday, June 26


4 credits

Course tuition


Enrollment status

  • Registration Closed
  • Prerequisites

    Two semesters of calculus. Placement test recommended.



    Oliver Knill, PhD.

    Preceptor in Mathematics, Harvard University