UW–Madison MATH 222: Calculus and Analytic Geometry 2
MATH 222 continues UW–Madison's main calculus sequence: techniques of integration, applications, sequences and series, Taylor series, and an introduction to vectors and parametric topics. Students widely consider it the harder half of the first-year sequence.
Fennie is independent and not affiliated with University of Wisconsin–Madison. This is an unofficial study guide.
Build my MATH 222 study planWhat makes it hard
Integration technique selection — knowing which method an unfamiliar integral wants — only develops through high practice volume, and the series unit is conceptually unlike all prior calculus: convergence reasoning is logic, not computation. The evening exams keep the time pressure, and students who scraped through 221 on weak fundamentals hit both walls hardest.
What you'll cover
- • Techniques of integration
- • Applications of integration
- • Improper integrals
- • Sequences and series
- • Convergence tests and Taylor series
- • Parametric equations and polar coordinates
The MATH 222 study guide
How to study for UW–Madison MATH 222, step by step.
- 1
Do mixed integral sets from week one
Technique selection is MATH 222's first exam skill and topic-sorted homework never builds it. Every practice session should mix substitution, parts, and partial fractions so the choice is forced.
- 2
Keep MATH 221 skills warm
Integration punishes weak differentiation and algebra twice over. A short weekly refresher prevents old gaps from resurfacing inside new material.
- 3
Start the series unit before it starts
Convergence reasoning needs more sittings than computation ever did. Read ahead before the unit opens and accept it will take repeated passes.
- 4
Build a convergence-test decision chart
Each test, its conditions, the series shapes it handles — one page. Practice classifying series rapidly with it, then without it; exams grade the choice as much as the execution.
- 5
Run old exams timed in the final week
The department's past evening exams are the closest match to the real event. Time pressure is part of what's tested — train under it deliberately.
- 6
Give both walls a schedule with Fennie
Upload your MATH 222 syllabus and Fennie's Daily Plan schedules daily mixed-technique practice and gives series extra runway, synced to evening exams, with quizzes generated from your actual course content. It's free to start.
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How Fennie helps with MATH 222
Fennie's Daily Plans pace MATH 222's two walls deliberately — daily mixed-integral practice for technique recognition, extra scheduled runway for the series unit — all synced to the evening exam calendar. Chat through which convergence test applies and why, the precise decision skill series questions test.
FAQ
Is MATH 222 harder than MATH 221?
Most UW students say yes: integration technique selection only comes from volume, and the series unit is a conceptual leap that catches even strong 221 students. Budget more weekly time than Calc I needed.
How do I study for the series unit in MATH 222?
Start before the unit opens, build a convergence-test decision chart, and practice classifying series before computing anything. The unit tests choosing the right tool under its right conditions, which formula drilling alone misses.
What comes after MATH 222?
MATH 234 (multivariable calculus) for most engineering and science tracks, with linear algebra (MATH 340 or 341) alongside or after depending on your major's plan. 234 assumes 222's integration fluency throughout.
Pass MATH 222 with a plan, not a cram
Upload your MATH 222 materials and Fennie generates a Daily Plan paced to your deadline — plus chat, flashcards, and quizzes built from the actual course content.
Get started freeMore UW–Madison courses
MATH 221 — Calculus and Analytic Geometry 1
MATH 221 is UW–Madison's five-credit Calculus I — limits, derivatives, applications of differentiation, and the beginnings of integration — required across engineering, the sciences, and quantitative majors, taught in large lectures with TA-led discussion sections and common evening exams.
MATH 234 — Calculus—Functions of Several Variables
MATH 234 is UW–Madison's multivariable calculus: vectors, partial derivatives, gradients, multiple integrals, and vector calculus through Green's and Stokes' theorems — the third course of the main calculus sequence, required across engineering and the physical sciences.
MATH 340 — Elementary Matrix and Linear Algebra
MATH 340 is UW–Madison's standard linear algebra course — systems of equations, matrix algebra, determinants, vector spaces, linear independence, eigenvalues, and diagonalization — the computational track taken by most engineering, CS, and science students (MATH 341 is the proof-based alternative).