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Multivariable Calculus
MATH 21A

Course Information

Description

To see how calculus applies in practical situations described by more than one variable, we study integration over curves, surfaces, and solid regions using different coordinate systems; parameterization of curves and surfaces; vectors, lines, and planes; partial derivatives and the gradient; constrained and unconstrained optimization; divergence and curl of vector fields; and the Green's, Stokes's, and Divergence Theorems.

There will be required workshops Tuesdays.

Course Notes

Math 21A is taught in small sections throughout the day on a Monday/Wednesday/Friday schedule (9:00-10:15 am, 10:30-11:45 am, 12-1:15 pm, 1:30-2:45 pm, and 3:00-4:15 pm with sufficient enrollment). Completing your registration for Math 21A is a two-step process: first, you'll enroll in the course within my.harvard, and then, you'll fill out the Math Sectioning form on the Math 21A Canvas page to submit your time preferences. Please submit time preferences before 11:59pm on Friday, 11/14. If your time preferences change, you may submit the form again; only your latest submission will be used. In order to receive your section assignment, you are required to take the Math 21A skills check. Please see the course's Canvas site for more information.

School Faculty of Arts & Sciences
Credits 4
Cross Reg

Available for Harvard Cross Registration

Department Mathematics
Course Component Lecture
Grading Basis FAS Letter Graded
Course Requirements Anti-requisite: Cannot be taken for credit if Math 18A or Math 22B already complete.
Exam/Final Deadline May 14, 2026
General Education N/A
Quantitative Reasoning with Data Yes
Divisional Distribution Science & Engineering & Applied Science
Course Level Primarily for Undergraduate Students