MATH 21A: Multivariable Calculus
Course exam catalog and study material archive for Multivariable Calculus at Harvard University. Request verified past exam papers and study resources directly through our student community.
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Common aliases: MATH 21A
Study Resources for Multivariable Calculus
Final Exam 2016
Midterm (Exam 1) 2012
Midterm (Exam 2) 2010
Midterm (Exam 1) 2014
Midterm (Exam 1) 2017
Quiz 3
Assessment Inventory for MATH 21A (6 Documents)
| Document | Format | Year | Access |
|---|---|---|---|
| Midterm (Exam 1) 2017 | Midterm | 2017 | Illustrative Archive |
| Final Exam 2016 | Final | 2016 | Illustrative Archive |
| Midterm (Exam 1) 2014 | Midterm | 2014 | Illustrative Archive |
| Midterm (Exam 1) 2012 | Midterm | 2012 | Illustrative Archive |
| Midterm (Exam 2) 2010 | Midterm | 2010 | Illustrative Archive |
| Quiz 3 | Quiz | — | Illustrative Archive |
Complete inventory of all 6 assessments (sorted by most recent). Select any document to inspect or use the search bar above to filter.
Course Overview & Exam Syllabus
This archive catalogs 6 free educational resources and past exams for MATH 21A (Multivariable Calculus) at Harvard University, containing 4 midterm papers, 1 final examination, and 1 quiz. Dated documents represent 5 distinct academic years between 2010 and 2017.
Core Exam Topics & Learning Objectives
- Three-dimensional geometry and vector algebra: dot products, cross products, planes, and parametric curves in MATH 21A
- Partial differentiation: tangent planes, directional derivatives, gradient vectors, and Lagrange multiplier optimization
- Multiple integration: double and triple integrals in Cartesian, cylindrical, and spherical coordinate systems
- Vector calculus theorems: line integrals, conservative fields, Green's Theorem, Stokes' Theorem, and Divergence Theorem in Multivariable Calculus
Frequently Asked Questions
Which assessment formats are cataloged in this MATH 21A archive?
This collection for MATH 21A at Harvard University catalogs 6 total resources across the following formats: Midterms, Finals, Quizzes. Each document is listed in the assessment inventory table with its individual format tag and academic year where recorded.
What academic years are covered in this MATH 21A collection?
Dated materials in this archive span from 2010 to 2017, representing 5 distinct academic years. Coverage varies by the records currently cataloged for this course.
How can students access these free MATH 21A past exams?
All cataloged MATH 21A past exams and study materials are free to request. The catalog, metadata, assessment inventory, and illustrative thumbnails are public; source documents are not shown on this page. Use the connect options to request a study resource, and confirm current course topics and grading policies with the Harvard University course syllabus.