# UGA MATH 2260 Calculus II: Syllabus, Topics and Practice

> A study guide for UGA MATH 2260 Calculus II for Science and Engineering: volumes, work, integration techniques, series and vectors.

Source: https://practicecalculus.com/courses/university-of-georgia-math-2260
Updated: 2026-11-08

## At a glance

- **Course code:** MATH 2260
- **Credit hours:** 4
- **Prerequisites:** MATH 2250 or MATH 2300H
- **Covers:** Volumes, arclength, work, separable differential equations, techniques of integration, sequences and series, convergence tests, power and Taylor series, vectors in 3D, dot and cross product, lines and planes
- **Duplicate credit:** Not open to students with credit in MATH 2410H or MATH 2410
- **Offered:** Fall, spring and summer every year
- **Next course:** MATH 2270 Calculus III for Science and Engineering
- **Practice here:** [Calculus 2](/learn/calculus-2)

## Key takeaways

- MATH 2260 is the 4-credit-hour Calculus II for Science and Engineering course at the University of Georgia.
- It covers volumes, arclength, work, separable differential equations, integration techniques, sequences and series, power series and Taylor series.
- It also introduces vectors in three-dimensional space, the dot and cross product, and lines and planes.
- The prerequisite is MATH 2250 or MATH 2300H.

**UGA MATH 2260** (Calculus II for Science and Engineering) is the second course in the University of Georgia's science and engineering calculus sequence. It is a 4-credit-hour course offered every fall, spring and summer, with MATH 2250 or MATH 2300H as the prerequisite. This guide maps the official topic list to lessons you can practice.

## What UGA MATH 2260 covers

The UGA Department of Mathematics describes MATH 2260 as: volumes, arclength, work, separable differential equations. Techniques of integration. Sequences and series, convergence tests, power series and Taylor series. Vectors in three-dimensional space, dot product, cross product, lines and planes.

So MATH 2260 is a full **Calculus 2** course plus a short unit on vectors that many other universities put in Calculus 3. The official description does not mention parametric equations or polar coordinates. A weekly schedule and textbook are set by the department and your instructor; the department page links a syllabi lookup.

## MATH 2260 topic map

| MATH 2260 topic | Practice | Read |
| --- | --- | --- |
| Volumes | [Volumes by disks](/learn/calculus-1/applications-of-integrals/volumes-disks) | [Volumes of revolution](/blog/volumes-of-revolution) |
| Arclength | [Arc length and surface area](/learn/calculus-2/improper-integrals-and-applications/arc-length-and-surface-area) | [Volumes by cross sections](/learn/calculus-1/applications-of-integrals/volumes-cross-sections) |
| Work | [Work](/learn/calculus-2/improper-integrals-and-applications/work) | [Definite integral properties](/rules/definite-integral-properties) |
| Separable differential equations | [Separable equations](/learn/calculus-2/improper-integrals-and-applications/separable-equations) | [Differential equations problems](/practice-problems/differential-equations) |
| Integration by parts | [Integration by parts](/learn/calculus-2/integration-techniques/integration-by-parts) | [Integration by parts](/blog/integration-by-parts) |
| Trig integrals and substitution | [Trig substitution](/learn/calculus-2/integration-techniques/trig-substitution) | [Trig substitution](/blog/trig-substitution) |
| Partial fractions | [Partial fractions](/learn/calculus-2/integration-techniques/partial-fractions) | [Partial fractions](/blog/partial-fractions) |
| Sequences | [Sequences](/learn/calculus-2/sequences-and-series/sequences) | [Geometric series](/blog/geometric-series) |
| Convergence tests | [Choosing a test](/learn/calculus-2/sequences-and-series/choosing-a-test) | [Convergence tests](/blog/convergence-tests) |
| Power series | [Power series and radius](/learn/calculus-2/power-series-parametric-polar/power-series-and-radius) | [Power series](/blog/power-series) |
| Taylor series | [Maclaurin series](/learn/calculus-2/power-series-parametric-polar/maclaurin-series) | [Taylor series](/blog/taylor-series) |
| Vectors, dot and cross product | [Dot product](/learn/calculus-3/vectors-and-space/dot-product) | [Dot and cross product](/blog/vectors-dot-and-cross-product) |
| Lines and planes | [Lines in space](/learn/calculus-3/vectors-and-space/lines-in-space) | [Planes in space](/learn/calculus-3/vectors-and-space/planes-in-space) |

## MATH 2260 in the UGA sequence

| Course | Credit hours | Prerequisite |
| --- | --- | --- |
| [MATH 2250 Calculus I for Science and Engineering](/courses/university-of-georgia-math-2250) | 4 | MATH 1113 or department permission |
| MATH 2260 Calculus II for Science and Engineering | 4 | MATH 2250 or MATH 2300H |
| [MATH 2270 Calculus III for Science and Engineering](/courses/university-of-georgia-math-2270) | 4 | MATH 2260, 2310H, 2410 or 2410H |

## How MATH 2260 builds on MATH 2250

MATH 2260 assumes you can differentiate quickly and evaluate definite integrals with the Fundamental Theorem of Calculus. It first uses integrals as a tool for volumes, lengths and work, then adds new techniques for harder integrals, then turns to infinite series, and finally steps into three dimensions with vectors. If your MATH 2250 integrals feel rusty, warm up with [antiderivative practice](/learn/calculus-1/integrals/antiderivative-practice) and [u-substitution](/learn/calculus-1/integrals/u-substitution).

## Example problems at the MATH 2260 level

**1. A volume by disks.** Rotating $y = \sqrt{x}$ on $[0, 4]$ about the $x$-axis:

$$V = \pi \int_0^4 x\,dx = 8\pi$$

**2. A separable equation.** If $\frac{dy}{dx} = \frac{x}{y}$, then $y\,dy = x\,dx$ and $y^2 - x^2 = C$.

**3. A dot product.** $\langle 2, -1, 3 \rangle \cdot \langle 1, 4, 2 \rangle = 2 - 4 + 6 = 4$.

## How to do well in MATH 2260

- **Draw every volume and work problem.** One labeled slice tells you the integral.
- **Practice choosing an integration technique** with [choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy).
- **Leave plenty of time for series.** Work through [series practice](/learn/calculus-2/sequences-and-series/series-practice) and [convergence tests problems](/practice-problems/convergence-tests).
- **Do not treat the vectors unit as an afterthought.** It is the foundation of MATH 2270.
- **Use timed [practice exams](/practice)** before each test.

> **Tip:** for a power series, find the radius with the ratio test, then check each endpoint separately. The endpoints often behave differently.

## Frequently asked questions

### What is MATH 2260 at UGA?

MATH 2260 Calculus II for Science and Engineering is UGA's second-semester calculus course. The department lists volumes, arclength, work, separable differential equations, techniques of integration, sequences and series, convergence tests, power series and Taylor series, plus vectors in three-dimensional space, the dot product, the cross product, and lines and planes.

### What is the prerequisite for MATH 2260?

MATH 2250 or MATH 2300H.

### Why does MATH 2260 include vectors?

At UGA, the introduction to vectors in three-dimensional space, including dot and cross products and lines and planes, is part of MATH 2260. That gives MATH 2270 more room for multivariable calculus.

### Can I take MATH 2260 if I have credit for MATH 2410?

No. MATH 2260 is not open to students with credit in MATH 2410 or MATH 2410H.

### What comes after MATH 2260?

MATH 2270 Calculus III for Science and Engineering, which lists MATH 2260, MATH 2310H, MATH 2410 or MATH 2410H as its prerequisite.