Ohio State MATH 1172 Engineering Math A: Study Guide, Practice

Ohio State MATH 1172, Engineering Mathematics A, is an engineering-oriented alternative to Calculus II at Ohio State. It is a 5-credit course that combines the core of Calculus 2 with an early start on multivariable calculus. This guide maps each MATH 1172 topic to practice with instant feedback.

What Ohio State MATH 1172 covers

The catalog lists techniques of integration, Taylor series and differential calculus of several variables, with applications. The department's course description document shows the order: applications of integration (regions between curves, volumes by slicing and shells, arc length, physical applications), then integration by parts, trig integrals, trig substitution, partial fractions and improper integrals.

Series are covered more briefly than in MATH 1152: sequences, the idea of convergence, the divergence test and the ratio test, leading to power series and Taylor series. The last third covers parametric and polar equations, conic sections, vectors in 2D and 3D, dot and cross products, curves in space and motion, and finally planes and surfaces, level curves, limits, partial derivatives, the chain rule, directional derivatives and the gradient.

In standard terms, MATH 1172 is most of Calculus 2 plus roughly the first third of Calculus 3.

MATH 1172 topic map

MATH 1172 vs MATH 1152

You can take only one of the two. The MATH 1152 guide covers the standard track, the MATH 1151 guide reviews the prerequisite, and the MATH 2153 guide shows what comes next.

Example problems at the MATH 1172 level

1. Repeated integration by parts. Evaluate \int x^2 e^x\,dx. Parts twice:

2. A Maclaurin series. Replace x with -x^2 in e^x = \sum \frac{x^n}{n!}:

3. A gradient. For f(x, y) = x^2 y - y^3 at (2, 1):

How to do well in Ohio State MATH 1172

• Keep up with the pace. Three different areas share one semester, so short daily sessions in techniques practice beat weekend cramming.
• Learn the ratio test well. It is the main convergence test in this course. The ratio test page has worked examples.
• Start thinking in 3D early. Vectors and partial derivatives come at the end, right before the final, and carry into MATH 2153.
• Practice by hand. The course page states that calculators are not permitted during exams. Use timed practice exams and the formula sheet while learning.
• Review common calculus mistakes before each midterm.

Tip: many Taylor series come from substituting into a known one, like e^x, \sin x or \frac{1}{1-x}, rather than computing derivatives from scratch.