UMN MATH 1272 Calculus II: Topics, Study Guide and Practice

MATH 1272 is Calculus II at the University of Minnesota Twin Cities, the second course in the sequence that starts with MATH 1271. It is a 4-credit course offered every fall, spring and summer, taken by students in science, engineering, math and economics who need more calculus. This guide maps every MATH 1272 topic to free practice, so you can learn each method by working problems with instant feedback.

What MATH 1272 covers

According to the University of Minnesota catalog, MATH 1272 covers techniques of integration and calculus involving transcendental functions and polar coordinates. It then moves on to Taylor polynomials and to the start of three-dimensional calculus: vectors, curves in space, and cylindrical and spherical coordinates.

Compared with a standard Calculus 2 course, MATH 1272 shares the integration techniques, polar coordinates and Taylor polynomials. Its catalog description does not list infinite series by name, but instead adds vectors and space curves, topics that many universities place at the start of Calculus 3. That gives MATH 2263 a head start.

MATH 1272 topic map

MATH 1272 vs MATH 1271 vs MATH 2263

If you are coming from MATH 1271, see the MATH 1271 guide for a refresher list. The MATH 2263 guide shows how the vectors you meet here turn into partial derivatives and multiple integrals.

Example problems at the MATH 1272 level

1. Integration by parts. Evaluate \int x\cos x\,dx with u = x and dv = \cos x\,dx, so du = dx and v = \sin x:

2. Partial fractions. Evaluate \int \frac{1}{x^2 - 1}\,dx. Since \frac{1}{(x-1)(x+1)} = \frac{1/2}{x-1} - \frac{1/2}{x+1}:

3. A Taylor polynomial. The degree 2 Taylor polynomial of e^x at 0 is T_2(x) = 1 + x + \frac{x^2}{2}. It estimates e^{0.1} \approx 1 + 0.1 + 0.005 = 1.105, while the true value is about 1.10517.

How to do well in MATH 1272

• Sort integrals before you solve them. Spend time on choosing a strategy: most exam integrals are hard only until you spot the technique.
• Memorize the core antiderivatives. Keep the calculus formula sheet open while practicing until the table is in your head.
• Check answers by differentiating. Every antiderivative can be verified in under a minute, which catches most sign and constant errors. Our common calculus mistakes list shows the usual traps.
• Get comfortable in three dimensions early. Vectors and space curves lead straight into MATH 2263, so practice the dot product and cross product now.
• Simulate exams with timed practice sets of mixed integrals.

Tip: if integration by parts keeps going in circles, use the LIATE order to pick u. Our repeated parts and LIATE lesson walks through it.