Harvard MATH 21B: Linear Algebra and Differential Equations
Math 21B covers linear algebra (systems, matrices, eigenvalues, orthogonality) and applies it to differential equations and Fourier series. It's a workhorse requirement for applied math, economics, CS, and science concentrators.
Fennie is independent and not affiliated with Harvard University. This is an unofficial study guide.
What makes it hard
The course shifts from computation to abstraction midway: row reduction is mechanical, but linear independence, subspaces, and eigenvector reasoning require a conceptual leap many students don't see coming. The differential equations finale then stacks new material on top of whatever linear algebra didn't fully solidify.
What you'll cover
- • Systems of linear equations and matrices
- • Linear transformations
- • Subspaces, basis, and dimension
- • Eigenvalues and eigenvectors
- • Orthogonality and least squares
- • Differential equations and Fourier series
The MATH 21B study guide
How to study for Harvard MATH 21B, step by step.
- 1
Attach a concept to every computation
Don't just find eigenvalues; articulate what they tell you about the transformation. Math 21B exam questions live at the junction between computing and understanding, so practice both together from week one.
- 2
Slow down for the subspace weeks
Linear independence, span, basis, and dimension are where 21B's abstraction leap happens, and it doesn't announce itself. Give those weeks extra time and build small concrete examples for every definition.
- 3
Test yourself with true/false concept questions
Ask whether a set of five vectors in R4 can be independent, or whether every matrix has an eigenvector. Conceptual quick-fire questions like these expose the gaps that pure computation practice hides.
- 4
Keep linear algebra warm into the differential equations finale
The ODE and Fourier material builds directly on eigenvalues and orthogonality. A weekly review of the earlier units prevents the end-of-semester stack-up the course is known for.
Today
Today's MATH 21B plan
What a Fennie Daily Plan looks like for MATH 21B. Yours is built from your own syllabus and adapts every day to your deadlines and progress.
First plan free, no card required. Fennie is independent and unaffiliated with your school.
FAQ
Is Math 21B harder than 21A?
Many students find 21B's abstraction harder than 21A's visualization, especially the subspace and eigenvalue material. The computational parts are straightforward; the concepts are the course.
Do I need Math 21B for CS at Harvard?
Linear algebra at the 21B level (or beyond) appears in the requirements or strong recommendations for CS and applied math tracks. Check current concentration requirements.
How do I study for Math 21B?
For every computation, attach the concept: don't just find eigenvalues, articulate what they tell you about the transformation. Exam questions live at exactly that junction.
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