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Multivariable Calculus
MATH 21A LEC

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 (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). Registering for Math 21A is a two-step process. Once enrolled, you must submit your time preferences before 5 pm on September 2 by filling out the Math Sectioning form in your To-Do list on my.harvard (this may take up to 15 minutes to appear after you enroll). 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 in-person on September 2. Please see the course's Canvas site for more information.

Class Notes

The QUIZ component of this course represents the designated time slot for your mid-term exams. While these exams do not occur weekly, it's important that this period remains on your schedule. If you encounter an academic conflict, you have the option to enroll in the TBA section. Students enrolled in the TBA section will be required to take all exams out of sequence.

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: Not to be taken in addition to AM 22b
Exam/Final Deadline Dec. 15, 2025
General Education N/A
Quantitative Reasoning with Data Yes
Divisional Distribution Science & Engineering & Applied Science
Course Level Primarily for Undergraduate Students