UCLA 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.
Fennie is independent and not affiliated with UCLA. This is an unofficial study guide.
What makes it hard
Series in a quarter system is the notorious combination: the most abstract topic in lower-division calculus, compressed into the final weeks before a cumulative final. 31B is widely cited by UCLA students as the hardest course in the 31/32 sequence, and exam medians reflect it.
What you'll cover
- • Integration by parts and partial fractions
- • Trigonometric integrals and substitution
- • Improper integrals
- • Sequences and infinite series
- • Convergence tests
- • Taylor and Maclaurin series
The MATH 31B study guide
How to study for UCLA MATH 31B, step by step.
- 1
Make integration automatic in the first five weeks
Students who struggle in MATH 31B are usually still shaky on integrals when series arrives. Daily technique drills early (parts, partial fractions, trig substitution) free your full attention for the back half.
- 2
Give series everything when it starts
Series is the most abstract topic in lower-division calculus, compressed into the final weeks of a ten-week quarter before a cumulative final. Classify several series daily from the moment the unit opens.
- 3
Build a convergence-test selection routine
Exam questions reward picking the right test fast. Practice classifying many series quickly rather than perfecting a few; speed of correct selection is the graded skill.
- 4
Memorize the standard Taylor series cold
The expansions for e^x, sin, cos, and the geometric series are assumed instant on the final. Flashcard them early so exam time goes to the hard parts.
Today
Today's MATH 31B plan
What a Fennie Daily Plan looks like for MATH 31B. 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 31B the hardest lower-division math class at UCLA?
It's the most common answer among students. Integration techniques demand pattern fluency, and the series unit is abstract material on a compressed timeline. The combination of both in ten weeks is what earns the reputation.
How do I pass MATH 31B?
Build integration fluency early through daily practice, so series gets your full attention in the back half. For convergence tests, practice classifying many series quickly rather than perfecting a few; exam questions reward fast correct test selection.
What comes after MATH 31B?
MATH 32A (multivariable differential calculus) for most STEM majors, with 32B and the 33 series after. 31B's series and integration skills return directly in 32B and differential equations.
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 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 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.
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.