UIUC MATH 231: Calculus II
MATH 231 covers techniques of integration, applications, and infinite sequences and series including Taylor series. It's the second course in UIUC's calculus sequence and a requirement for engineering, CS, and physical science majors, with many students placing into it via AP credit.
Fennie is independent and not affiliated with University of Illinois Urbana-Champaign. This is an unofficial study guide.
What makes it hard
Series is the universal Calc II wall and UIUC is no exception: the convergence-test unit is abstract, fast, and worth a large share of the final. Students entering via AP credit who skipped a semester of college exam habits often find 231 their first real calibration shock.
What you'll cover
- • Integration techniques
- • Improper integrals
- • Applications of integration
- • Sequences and infinite series
- • Convergence tests
- • Taylor and Maclaurin series
The MATH 231 study guide
How to study for UIUC MATH 231, step by step.
- 1
Recalibrate if you placed in via AP credit
Many MATH 231 students skipped a semester of college exam habits, and 231 is often their first calibration shock. Treat the first weeks as learning UIUC's exam style, not just the content.
- 2
Get integration reflexive before series arrives
Technique fluency is assumed quickly, and the series unit needs your undivided attention when it lands. Daily integration drills early in the semester buy you that bandwidth.
- 3
Classify many series fast, not a few perfectly
Build a decision order for convergence tests and run it on dozens of examples until selection is automatic. That single skill is the largest point block on most finals.
- 4
Lock in the standard series facts
Geometric series, p-series thresholds, and the standard Taylor series belong on flashcards from the day they appear. The final assumes these expansions and test conditions are instant.
Today's MATH 231 plan
What a Fennie Daily Plan looks like for MATH 231. Yours is built from your syllabus and adapts every day to your deadlines and progress.
- Review: Improper integralsReview · 25 min
Work back through the MATH 231 material on improper integrals. In the app, Fennie builds this from your own notes and syllabus.
- Practice: Applications of integrationPractice · 20 min
Targeted problems on applications of integration, the kind MATH 231 actually tests.
- Quick quiz: Sequences and infinite seriesQuiz · 10 min
Five generated questions to expose weak spots on sequences and infinite series before the exam does.
- Preview: Convergence testsPreview · 10 min
A first pass over convergence tests so the next session starts from familiar ground.
First plan free, no card required. Fennie is independent and unaffiliated with your school.
FAQ
Is MATH 231 harder than MATH 221?
Most students say yes. Series is more abstract than anything in Calc I, and integration technique fluency is assumed quickly. It's also many AP-credit students' first UIUC math course, which adds an adjustment factor independent of content.
How do I pass the series unit in MATH 231?
Classify many series fast rather than a few perfectly: build a decision order for convergence tests and apply it to dozens of examples until selection is automatic. That single skill is the largest point block on most finals.
What comes after MATH 231 at UIUC?
MATH 241 (Calculus III) for most STEM majors, plus MATH 285 or 286 (differential equations) for engineering tracks. The Taylor series material from 231 reappears directly in both.
More UIUC courses
MATH 221: Calculus I
MATH 221 is UIUC's first calculus course, covering limits, derivatives, applications, and the beginnings of integration, required across engineering, science, and CS. It's a large-lecture course with discussion sections and online homework, taken by a huge share of incoming STEM students.
MATH 241: Calculus III
MATH 241 is UIUC's multivariable calculus course: vectors, partial derivatives, multiple integrals, and vector calculus through Green's, Stokes', and the divergence theorems. It's required for engineering, physics, math, and many CS-adjacent tracks.
MATH 257: Linear Algebra with Computational Applications
MATH 257 is UIUC's modern linear algebra course, covering linear systems, matrix operations, vector spaces, eigenvalues, orthogonality, least squares, and the SVD, taught with computational labs in Python. It replaced MATH 415 in most engineering and CS-adjacent curricula, pairing the theory with the data-scale applications that motivate it.
MATH 285: Introduction to Differential Equations
MATH 285 is UIUC's differential equations course for engineering and science majors: first and second-order ODEs, applications like oscillations and circuits, plus Fourier series and an introduction to boundary value problems and partial differential equations. It typically follows MATH 241 in the engineering math core.