MIT 18.02: Multivariable Calculus
18.02 is MIT's multivariable calculus GIR: vectors, partial derivatives, multiple integrals, and vector calculus through Green's, Stokes', and the divergence theorems. It's required for every MIT student and is among the most-viewed math courses on OpenCourseWare.
Fennie is independent and not affiliated with MIT. This is an unofficial study guide.
What makes it hard
The vector calculus finale is the wall: line and surface integrals, and knowing which of the three big theorems applies where. Setting up integrals over 3D regions requires spatial reasoning that some students need weeks of deliberate practice to build.
What you'll cover
- • Vectors and matrices
- • Partial derivatives and gradients
- • Optimization and Lagrange multipliers
- • Double and triple integrals
- • Line integrals and Green's theorem
- • Stokes' theorem and the divergence theorem
The 18.02 study guide
How to study for MIT 18.02, step by step.
- 1
Drill integral setups without solving them
Given a 3D region described in words, write the bounds (multiple orders, multiple coordinate systems), then stop. Setup is where 18.02 exam points are won, and you can do ten setups in the time one full solution takes.
- 2
Sketch every region and surface
The spatial reasoning that 18.02 demands is built through deliberate drawing practice, not staring at formulas. A rough sketch per problem, every time, for weeks. It compounds.
- 3
Bank extra time for the vector calculus finale
Line integrals, surface integrals, and choosing among Green's, Stokes', and the divergence theorems form the wall at the end. Start that material early; knowing which theorem applies where is its own skill.
- 4
Benchmark against OCW exams, solutions after
OCW posts 18.02 exams with solutions. Take them timed, attempt every problem honestly, and only then study the solutions. The comparison shows whether your setups match MIT's expectations.
Today
Today's 18.02 plan
What a Fennie Daily Plan looks like for 18.02. 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 18.02 harder than 18.01?
Most students find the visualization demands harder, especially the final vector calculus unit. The computation is similar; the setup is the challenge.
How long does 18.02 take on OCW?
A full self-study pass typically takes 12-14 weeks at 8-10 hours per week, with the last third deserving the most time.
Do I need 18.01 before 18.02?
Yes. 18.02 assumes complete fluency with single-variable differentiation and integration from day one.
More MIT courses
18.01: Single Variable Calculus
18.01 is MIT's single-variable calculus GIR, covering limits, differentiation, integration, and infinite series, required of every MIT student without prior credit. The OCW version, including David Jerison's lectures, has taught calculus to millions of self-learners.
18.06: Linear Algebra
18.06 is MIT's linear algebra course, made world-famous by Gilbert Strang, whose OCW lectures are arguably the most beloved math course recordings ever published. It covers systems of equations, vector spaces, orthogonality, determinants, eigenvalues, and the SVD with Strang's signature intuition-first style.
18.03: Differential Equations
18.03 is MIT's differential equations course, covering first and second order ODEs, Laplace transforms, Fourier series, and linear systems. It's required by most engineering and science majors and among the most-used math courses on OpenCourseWare, where Arthur Mattuck's lectures are a classic.
18.05: Introduction to Probability and Statistics
18.05 is MIT's introduction to probability and statistics: probability models, random variables, Bayesian and frequentist inference, and regression, taught in a celebrated flipped, problem-centered format whose complete materials on OCW make it one of the most recommended statistics self-study courses anywhere.