UNC MATH 232 Calculus II: Syllabus, Topics and Practice

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 in the UNC sequence

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 and u-substitution before the first homework is due.

Example problems at the MATH 232 level

1. Partial fractions.

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

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 lesson trains exactly this.
• Start series early. It is usually the last unit and the one students underestimate. Work through 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 and Taylor series problems.
• Take timed practice exams 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.