Princeton MAT 104: Calculus II
MAT 104 is Princeton's Calculus II — integration techniques, applications of integrals, sequences and series, and parametric and polar topics — continuing from MAT 103 for students across the sciences, economics, and engineering-adjacent tracks.
Fennie is independent and not affiliated with Princeton University. This is an unofficial study guide.
Build my MAT 104 study planWhat makes it hard
Two distinct walls: integration techniques demand pattern recognition that only volume builds — knowing which method fits which integral — and the series unit (convergence tests, Taylor series) is conceptually unlike anything before it. Students who scraped through Calc I on weak fundamentals usually hit the harder wall here.
What you'll cover
- • Techniques of integration
- • Applications of integration
- • Improper integrals
- • Sequences and series
- • Convergence tests
- • Taylor and power series
The MAT 104 study guide
How to study for Princeton MAT 104, step by step.
- 1
Do mixed integral sets from week one
Technique selection — substitution, parts, or partial fractions — is MAT 104's first exam skill, built only by large volumes of mixed practice, never by topic-sorted homework alone.
- 2
Keep Calc I skills warm
Integration punishes weak differentiation and algebra twice as hard. A short weekly refresher prevents old gaps from resurfacing on new material.
- 3
Give the series unit double runway
Sequences and series is a conceptual leap unlike anything before it. Start reading ahead before the unit opens, and accept that convergence reasoning needs more sittings than computation ever did.
- 4
Build a convergence-test decision chart
One page: each test, its conditions, and the series shapes it handles. Practice classifying series rapidly with the chart, then without it — exams test the choice as much as the execution.
- 5
Build the reps on a Fennie Daily Plan
Upload your MAT 104 syllabus and Fennie schedules daily mixed-technique practice paced to the exams, with the series unit given extra runway and quizzes generated from your actual course content. Free to start.
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How Fennie helps with MAT 104
Fennie's Daily Plans build the integral-pattern reps MAT 104 actually requires — daily mixed-technique practice paced to the exams, with the series unit given the extra runway it deserves. Chat through which convergence test applies and why, the exact decision skill series exam questions test.
FAQ
Is MAT 104 harder than MAT 103?
Most students say yes. Integration techniques require recognizing which method fits each problem — a skill only built by volume — and the sequences and series unit is a conceptual leap that catches even students who did fine in Calc I.
How do I study for MAT 104 series?
Build a decision chart of convergence tests and practice classifying series rapidly before computing anything — the choice of test is the exam skill. The series unit is more logic than computation, so it rewards conceptual understanding over formula drilling.
What comes after MAT 104?
Typically MAT 201 (Multivariable Calculus) and MAT 202 (Linear Algebra) for students continuing in quantitative fields. Your major and placement determine the exact path, so check the math department's sequence guidance.
Pass MAT 104 with a plan, not a cram
Upload your MAT 104 materials and Fennie generates a Daily Plan paced to your deadline — plus chat, flashcards, and quizzes built from the actual course content.
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MAT 103 — Calculus I
MAT 103 is Princeton's introductory Calculus I — limits, derivatives, applications of differentiation, and an introduction to integration — for students who need a calculus foundation before continuing in the sequence or supporting science and economics coursework.
MAT 201 — Multivariable Calculus
MAT 201 is Princeton's multivariable calculus course — vectors and the geometry of space, partial derivatives, multiple integrals, and vector calculus including line and surface integrals and the major theorems. It follows the single-variable sequence for students in quantitative fields.
MAT 202 — Linear Algebra with Applications
MAT 202 is Princeton's applied linear algebra course — systems of equations, matrices, vector spaces, linear transformations, eigenvalues and eigenvectors, and orthogonality, with applications across science and engineering. It's a common requirement for quantitative majors.
MAT 175 — Mathematics for Economics/Life Sciences
MAT 175 is Princeton's calculus course tailored for economics and life-science students — differentiation, optimization, integration, and selected multivariable and applied topics with examples drawn from those fields. It satisfies calculus requirements for majors that don't need the full math-track sequence.