ASU MAT 266 Calculus for Engineers II: Study Guide and Practice

ASU MAT 266, Calculus for Engineers II, is the second course in Arizona State University's engineering calculus sequence. It follows MAT 265 and finishes single-variable calculus with integration techniques, applications and Taylor series. This guide maps every MAT 266 topic to a lesson you can practice with instant feedback.

What ASU MAT 266 covers

The ASU catalog lists methods of integration, applications of calculus, elements of analytic geometry, improper integrals and Taylor series. It is a 3-credit-hour course that counts toward Mathematical Studies.

That is a standard Calculus 2. "Elements of analytic geometry" typically means curves such as conics, and parametric and polar descriptions of curves. Taylor series are the main series topic named, so expect convergence ideas to appear in support of them. On PracticeCalculus, MAT 266 lines up with the Calculus 2 path.

The course splits naturally into two halves. The first is about integration: learning substitution, parts, trigonometric integrals and partial fractions, then applying integrals to areas, volumes, arc length and work, and extending them to improper integrals over infinite intervals. The second half turns to curves and approximation: describing curves with analytic geometry, then representing functions as Taylor series. Students who keep practicing the first half while learning the second tend to find the final exam far less stressful.

MAT 266 topic map

MAT 266 among ASU's second-semester options

Example problems at the MAT 266 level

1. An improper integral.

2. Partial fractions. Since \frac{1}{x(x + 1)} = \frac{1}{x} - \frac{1}{x + 1},

3. A Maclaurin series. The derivatives of \sin x at 0 cycle through 0, 1, 0, -1, so

How to do well in MAT 266

• Practice choosing the technique. The choosing a strategy lesson mixes methods the way exams do.
• Learn LIATE for parts. Picking u well is most of the battle. See repeated parts and LIATE.
• Memorize five Maclaurin series: e^x, \sin x, \cos x, \ln(1 + x) and \frac{1}{1-x}. New series are usually built from these.
• Keep the formula sheet open for trig identities, review common calculus mistakes, and use timed practice exams.

Tip: an improper integral is just a limit of ordinary integrals. Write the limit explicitly every time and the convergence question answers itself.