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UVA MATH 1320: Calculus II

MATH 1320 continues the College's calculus sequence with techniques of integration, applications of the integral, sequences and series, and parametric and polar topics. It's widely considered the harder half of the sequence and a prerequisite gateway for math, economics, and science tracks.

Fennie is independent and not affiliated with University of Virginia. This is an unofficial study guide.

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What makes it hard

Integration techniques demand pattern recognition — knowing which method an integral wants — that only mixed-practice volume builds. Then sequences and series arrive: the first calculus material that's more logic than computation, where convergence arguments blindside students who've studied by drilling procedures. Many strong MATH 1310 students call this their hardest semester of math.

What you'll cover

  • • Techniques of integration
  • • Applications of integration
  • • Improper integrals
  • • Sequences and series
  • • Convergence tests
  • • Taylor and power series

The MATH 1320 study guide

How to study for UVA MATH 1320, step by step.

  1. 1

    Mix your integral practice from week one

    Topic-sorted homework hides the real exam skill: deciding which technique an unlabeled integral wants. Do mixed sets early and often so technique selection becomes the trained reflex it needs to be.

  2. 2

    Keep differentiation and algebra warm

    Integration punishes weak MATH 1310 skills twice over — every substitution and parts problem runs derivatives in reverse. A brief weekly refresher prevents old gaps from resurfacing on new material.

  3. 3

    Give series double the runway you think it needs

    Convergence reasoning is unlike anything before it and needs more sittings, not longer ones. Start reading ahead before the unit opens and accept slower progress as normal.

  4. 4

    Build a one-page convergence-test decision chart

    Each test, its hypotheses, and the series shapes it handles, side by side. Practice classifying series quickly with the chart, then without — exams grade the choice of test as much as the execution.

  5. 5

    Rehearse under time before each exam

    Mixed integrals and series questions, timed, no notes. The pattern-recognition the course builds has to perform at exam pace, and untimed homework never tests that.

  6. 6

    Let Fennie pace the volume

    Upload your MATH 1320 syllabus and Fennie's Daily Plan schedules daily mixed-technique integral practice and gives the series unit extra runway, all paced to your exams, with quizzes built from the actual course content. Free to start.

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How Fennie helps with MATH 1320

Fennie's Daily Plans build the two skills MATH 1320 actually grades: integral pattern-recognition through daily mixed practice, and convergence reasoning through a series unit given proper runway — all paced to exam dates. Chat through which test applies to a series and why, since the exams grade the decision as much as the computation.

FAQ

Is MATH 1320 harder than MATH 1310?

Most students say clearly yes. Technique selection on integrals only comes from volume, and sequences and series is a conceptual leap — the first calculus unit that's more logic than procedure. Students who scraped through 1310 on weak fundamentals tend to hit the wall here.

How do I study for the series unit in MATH 1320?

Start before the unit opens, build a decision chart of convergence tests with their conditions, and practice classifying series rapidly before computing anything. Expect it to need more separate sittings than earlier material — convergence reasoning accumulates slowly and can't be crammed.

What does MATH 1320 unlock?

It's the prerequisite gateway for multivariable calculus (MATH 2310), linear algebra (MATH 3351), statistics coursework, and the math expectations of economics and science majors. Programs across the College assume 1320-level fluency, so genuine mastery pays compound interest.

Pass MATH 1320 with a plan, not a cram

Upload your MATH 1320 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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More UVA courses

MATH 1310 — Calculus I

MATH 1310 is the College of Arts & Sciences' Calculus I — limits, derivatives, applications of differentiation, and the beginnings of integration — serving math, science, economics, and pre-health tracks. Engineering students take the parallel APMA sequence instead.

MATH 2310 — Calculus III

MATH 2310 is multivariable calculus for the College — vectors, partial derivatives, multiple integrals, and the vector calculus capstones (line and surface integrals, Green's and Stokes' theorems). It's required or expected for math, physics, economics-quantitative, and CS-adjacent tracks.

MATH 3351 — Elementary Linear Algebra

MATH 3351 is the math department's linear algebra course — matrices and row operations, vector spaces and bases, orthogonality, linear transformations, and eigenvalues — with deliberate emphasis on theory and abstract argument rather than pure computation. Credit isn't given for both MATH 3350 and 3351.