UCLA MATH 32B: Calculus of Several Variables
MATH 32B completes UCLA's multivariable calculus sequence: multiple integrals, change of variables, line and surface integrals, and the vector-calculus theorems of Green, Stokes, and Gauss. It follows 32A and is required across engineering and the physical sciences.
Fennie is independent and not affiliated with UCLA. This is an unofficial study guide.
What makes it hard
The vector-calculus finale is where grades are decided: line and surface integrals demand setup judgment and 3D visualization, and the three big theorems blur together for anyone who learned them as formulas. The ten-week pace lands all of it in the back half, right before a cumulative final.
What you'll cover
- • Double and triple integrals
- • Change of variables and Jacobians
- • Vector fields and line integrals
- • Green's theorem
- • Surface integrals and flux
- • Stokes' theorem and the divergence theorem
The MATH 32B study guide
How to study for UCLA MATH 32B, step by step.
- 1
Sketch the region before every integral
Most 32B points die at setup: wrong bounds, wrong order, wrong coordinate system. Drawing the region or surface first is the habit that fixes that, so make it step one of every problem.
- 2
Build fluency in all three coordinate systems early
Cartesian, cylindrical, and spherical setups plus Jacobians are the daily arithmetic. Drill switching between them in the first weeks so the back-half theorems don't compound a coordinate weakness.
- 3
Learn Green's, Stokes', and divergence as one family
They all relate a region to its boundary. Build a one-page comparison of when each applies and what each converts; exams love asking which theorem fits the scenario.
- 4
Work your instructor's past exams timed
Exam style varies by professor and the quarter puts the final right after the second midterm. Timed past exams from your instructor are the most efficient prep for the compressed back half.
Today
Today's MATH 32B plan
What a Fennie Daily Plan looks like for MATH 32B. 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 32B hard at UCLA?
The integration mechanics are manageable; the vector-calculus theorems in the back half are where difficulty concentrates, compressed into a ten-week quarter before a cumulative final. Students who practice setup and visualization steadily handle it; formula memorizers hit the wall.
What's the hardest topic in MATH 32B?
Line and surface integrals and choosing among Green's, Stokes', and the divergence theorem. Setting up the integral correctly is the hard part (the computation afterward is routine), so practice setup as its own skill.
Do I need MATH 32A before 32B?
Yes. 32A is the enforced prerequisite, and 32B assumes its vectors, partial derivatives, and gradients from day one. The sequence is designed to be taken back-to-back.
More UCLA courses
MATH 31A: Differential and Integral Calculus
MATH 31A is UCLA's first calculus course, covering limits, derivatives, optimization, and the basics of integration, required across engineering, physical science, economics, and life-science-adjacent tracks. Most STEM freshmen take it (or skip it via AP credit) in fall quarter.
MATH 31B: Integration and Infinite Series
MATH 31B covers integration techniques, applications, improper integrals, and infinite sequences and series including Taylor series. It's the second course in UCLA's main calculus sequence and a prerequisite for the multivariable courses that follow.
MATH 32A: Calculus of Several Variables
MATH 32A introduces multivariable calculus: vectors, vector-valued functions, partial derivatives, gradients, and optimization in several variables. It's required for engineering, physics, math, and CS-adjacent tracks, typically taken in the first year after the 31 sequence.
MATH 33A: Linear Algebra and Applications
MATH 33A is UCLA's linear algebra course: systems of equations, matrices, vector spaces, linear transformations, orthogonality, least squares, eigenvalues, and eigenvectors. It's required across engineering, math, and CS, and the linear algebra it teaches underpins machine learning and upper-division applied coursework.