# UNC MATH 232 Calculus II: Syllabus, Topics and Practice

> A study guide for UNC Chapel Hill MATH 232: integration techniques, improper integrals, series, Taylor's formula and differential equations.

Source: https://practicecalculus.com/courses/unc-chapel-hill-math-232
Updated: 2026-11-08

## At a glance

- **Course code:** MATH 232
- **Credits:** 4
- **Prerequisites:** A grade of C- or better in MATH 231, or placement by the department
- **Covers:** Techniques of integration, numerical integration, applications of integration, improper integrals, sequences, series, power series, Taylor's formula, elementary differential equations
- **Gen Ed:** IDEAs in Action FC-QUANT (FY-LAUNCH in designated sections)
- **Next course:** MATH 233 Calculus of Functions of Several Variables
- **Practice here:** [Calculus 2](/learn/calculus-2)

## Key takeaways

- MATH 232 is the 4-credit Calculus II course at UNC Chapel Hill.
- It covers techniques of integration, numerical integration, applications of integration, improper integrals, sequences and series, power series, Taylor's formula and elementary differential equations.
- You need a C- or better in MATH 231, or placement by the department.
- MATH 232 is the prerequisite for MATH 233 Calculus of Functions of Several Variables.

**UNC MATH 232** (Calculus of Functions of One Variable II) is the second course in the UNC Chapel Hill calculus sequence. It carries 4 credits, meets the FC-QUANT requirement, and needs a C- or better in MATH 231 or placement by the department. This guide maps each topic in the official description to a lesson you can practice.

## What UNC MATH 232 covers

The UNC mathematics department describes MATH 232 as: techniques of integration, numerical integration, applications of integration, improper integrals, sequences, series, power series, Taylor's formula, elementary differential equations. An honors version is available.

That is a full **Calculus 2** course. Notice that elementary differential equations are part of the description, so expect topics such as separable equations and growth and decay models. The listing does not mention parametric equations or polar coordinates, and it does not give a schedule or textbook, so check your section syllabus for those details.

## MATH 232 topic map

| MATH 232 topic | Practice | Read |
| --- | --- | --- |
| Substitution review | [u-substitution refresher](/learn/calculus-2/integration-techniques/u-substitution-refresher) | [u-substitution](/blog/u-substitution) |
| 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 integrals](/learn/calculus-2/integration-techniques/trig-integrals) | [Trig substitution](/blog/trig-substitution) |
| Partial fractions | [Partial fractions](/learn/calculus-2/integration-techniques/partial-fractions) | [Partial fractions](/blog/partial-fractions) |
| Numerical integration | [Trapezoid sums](/learn/calculus-1/integrals/trapezoid-sums) | [Riemann sums](/blog/riemann-sums) |
| Applications of integration | [Volumes by washers](/learn/calculus-1/applications-of-integrals/volumes-washers) | [Volumes of revolution](/blog/volumes-of-revolution) |
| Arc length and work | [Arc length and surface area](/learn/calculus-2/improper-integrals-and-applications/arc-length-and-surface-area) | [Work](/learn/calculus-2/improper-integrals-and-applications/work) |
| Improper integrals | [Infinite discontinuities](/learn/calculus-2/improper-integrals-and-applications/infinite-discontinuities) | [Improper integrals](/blog/improper-integrals) |
| Sequences | [Sequences](/learn/calculus-2/sequences-and-series/sequences) | [Convergence tests](/blog/convergence-tests) |
| Series | [Ratio and root tests](/learn/calculus-2/sequences-and-series/ratio-and-root-tests) | [Geometric series](/blog/geometric-series) |
| Power series | [Power series and radius](/learn/calculus-2/power-series-parametric-polar/power-series-and-radius) | [Power series](/blog/power-series) |
| Taylor's formula | [Taylor polynomials](/learn/calculus-2/power-series-parametric-polar/taylor-polynomials) | [Taylor series](/blog/taylor-series), [Taylor's theorem](/theorems/taylors-theorem) |
| Elementary differential equations | [Separable equations](/learn/calculus-2/improper-integrals-and-applications/separable-equations) | [Growth and decay](/learn/calculus-2/improper-integrals-and-applications/growth-and-decay) |

## MATH 232 in the UNC sequence

| Course | Credits | Prerequisite |
| --- | --- | --- |
| [MATH 231](/courses/unc-chapel-hill-math-231) Calculus of Functions of One Variable I | 4 | MATH 110 and 130 (C- in 130) or placement |
| MATH 232 Calculus of Functions of One Variable II | 4 | C- in MATH 231 or placement |
| [MATH 233](/courses/unc-chapel-hill-math-233) Calculus of Functions of Several Variables | 4 | MATH 232 |

## How MATH 232 builds on MATH 231

MATH 232 assumes you can find derivatives quickly and evaluate simple integrals with the Fundamental Theorem of Calculus. The first weeks add new integration techniques, and the rest of the course uses integrals as a tool: to measure volumes and lengths, to decide whether an improper integral is finite, and to test infinite series. If MATH 231 feels far away, review [antiderivative practice](/learn/calculus-1/integrals/antiderivative-practice) and [u-substitution](/learn/calculus-1/integrals/u-substitution) before the first homework is due.

## Example problems at the MATH 232 level

**1. Partial fractions.**

$$\int \frac{1}{x(x+1)}\,dx = \int \left(\frac{1}{x} - \frac{1}{x+1}\right)dx = \ln\left|\frac{x}{x+1}\right| + C$$

**2. A Taylor polynomial.** The degree 3 Maclaurin polynomial of $e^x$ is

$$1 + x + \frac{x^2}{2} + \frac{x^3}{6}$$

**3. A separable differential equation.** If $y' = 2y$ and $y(0) = 5$, then $y = 5e^{2x}$.

## How to do well in MATH 232

- **Build a technique checklist:** substitution first, then parts, trig methods, and partial fractions. The [choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy) lesson trains exactly this.
- **Start series early.** It is usually the last unit and the one students underestimate. Work through [choosing a test](/learn/calculus-2/sequences-and-series/choosing-a-test) more than once.
- **Memorize a few key Maclaurin series** ($e^x$, $\sin x$, $\cos x$, $\frac{1}{1-x}$) and build others from them.
- **Practice with [convergence tests problems](/practice-problems/convergence-tests)** and [Taylor series problems](/practice-problems/taylor-series).
- **Take timed [practice exams](/practice)** before each midterm and the final.

> **Tip:** when the ratio test gives a limit of exactly $1$, it tells you nothing. Switch to a comparison, integral or alternating series test.

## Frequently asked questions

### What is MATH 232 at UNC?

MATH 232 Calculus of Functions of One Variable II is UNC Chapel Hill's second-semester calculus course. The department lists techniques of integration, numerical integration, applications of integration, improper integrals, sequences, series, power series, Taylor's formula and elementary differential equations. An honors version is available.

### What is the prerequisite for MATH 232?

A grade of C- or better in MATH 231, or placement by the department.

### Can AP credit place me into MATH 232?

The prerequisite allows placement by the department as an alternative to MATH 231. Check the UNC math placement information for how AP or other credit is applied.

### What is the hardest part of MATH 232?

Most students find series the hardest part, because each problem needs you to choose the right convergence test. Integration techniques are the second big hurdle for the same reason.

### What comes after MATH 232?

MATH 233 Calculus of Functions of Several Variables, which lists MATH 232 as its prerequisite.