Cornell MATH 1120 Calculus II: Topics, Study Guide and Practice

Cornell MATH 1120 is Calculus II at Cornell University, the course most non-engineering students take after MATH 1110. It completes single-variable calculus: integration in depth, a first look at differential equations, and infinite series. Every MATH 1120 topic is mapped below to a lesson you can practice with instant feedback.

What Cornell MATH 1120 covers

According to the Cornell class roster, MATH 1120 centers on integration: applications such as volumes and arc length, techniques of integration, approximate integration with error estimates, improper integrals, and differential equations with their applications. It then covers infinite sequences and series, including the definition and tests for convergence, power series, Taylor series with remainder, and parametric equations.

That is a standard Calculus 2, with slightly more emphasis on differential equations and numerical integration than many courses. Polar coordinates are not named in the roster description.

MATH 1120 topic map

MATH 1120 vs MATH 1910

The content overlaps heavily, which is why the two are forbidden overlaps. Before MATH 1120 comes MATH 1110 Calculus I. Students on the math major path later take MATH 2220 Multivariable Calculus after linear algebra.

Example problems at the MATH 1120 level

1. Integration by parts. Evaluate \int x e^{2x}\,dx with u = x, dv = e^{2x}\,dx, so v = \frac{1}{2}e^{2x}:

2. A separable differential equation. Solve \frac{dy}{dx} = 3y with y(0) = 2.

Separate: \frac{dy}{y} = 3\,dx, so \ln|y| = 3x + C and y = Ae^{3x}. The initial condition gives A = 2, so y = 2e^{3x}.

3. Arc length. The length of y = \frac{2}{3}x^{3/2} from x = 0 to x = 3: since y' = x^{1/2},

How to do well in MATH 1120

• Build a technique checklist. Substitution, parts, trig integrals, trig substitution, partial fractions. Practice choosing a strategy until picking the method is quick.
• Understand the remainder, not just the series. Taylor series with remainder is named in the roster, so practice bounding errors with Taylor's theorem.
• Use the comparison families. The geometric series formula and p-series power most convergence arguments, along with the ratio test.
• Keep the formula sheet next to you, review common calculus mistakes, and finish each unit with a timed practice exam.

Tip: when an integral looks impossible, check for a substitution first. Many Calculus II integrals that look like they need parts are really u-substitution in disguise.