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

> A study guide for Ohio State MATH 1172 (Engineering Mathematics A): integration techniques, Taylor series and an intro to several-variable calculus.

Source: https://practicecalculus.com/courses/ohio-state-math-1172
Updated: 2026-11-03

## At a glance

- **Course code:** MATH 1172
- **Credit hours:** 5
- **Offered:** Autumn, spring and summer
- **Prerequisites:** C- or above in MATH 1114 (114), 1151, 1156, 1161.xx, 152.xx, 161.xx or 161.01H
- **Covers:** Techniques of integration, Taylor series, differential calculus of several variables, with applications
- **Restrictions:** Not open to math, pre-actuarial or actuarial science majors, or to students with credit for MATH 1152
- **Next course:** MATH 2153 (Calculus III)
- **Practice here:** [Calculus 2](/learn/calculus-2) and the start of [Calculus 3](/learn/calculus-3)

## Key takeaways

- MATH 1172, Engineering Mathematics A, is a 5-credit Ohio State course taken after Calculus I as an alternative to MATH 1152.
- It covers integration techniques, Taylor series, and differential calculus of several variables.
- You cannot take both MATH 1172 and MATH 1152, and math, pre-actuarial and actuarial science majors cannot take 1172.
- Like MATH 1152, it leads to MATH 2153, Calculus III.

**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 topic | Practice | Read |
| --- | --- | --- |
| Areas and volumes | [Volumes with washers](/learn/calculus-1/applications-of-integrals/volumes-washers) | [Volumes of revolution](/blog/volumes-of-revolution) |
| Arc length and physical applications | [Arc length and surface area](/learn/calculus-2/improper-integrals-and-applications/arc-length-and-surface-area) | [Center of mass](/learn/calculus-2/improper-integrals-and-applications/center-of-mass) |
| Integration by parts | [Repeated parts and LIATE](/learn/calculus-2/integration-techniques/repeated-parts-and-liate) | [Integration by parts](/blog/integration-by-parts) |
| Trig integrals and substitution | [Powers of sine and cosine](/learn/calculus-2/integration-techniques/trig-integrals) | [Trig substitution](/blog/trig-substitution) |
| Partial fractions | [Partial fractions](/learn/calculus-2/integration-techniques/partial-fractions) | [Partial fractions](/blog/partial-fractions) |
| Improper integrals | [Integrating to infinity](/learn/calculus-2/improper-integrals-and-applications/infinite-limits-of-integration) | [Improper integrals](/blog/improper-integrals) |
| Series, divergence and ratio tests | [The nth-term test](/learn/calculus-2/sequences-and-series/nth-term-test) | [nth-term test](/rules/nth-term-test), [ratio test](/rules/ratio-test) |
| Power and Taylor series | [Taylor polynomials](/learn/calculus-2/power-series-parametric-polar/taylor-polynomials) | [Taylor series](/blog/taylor-series), [Taylor's theorem](/theorems/taylors-theorem) |
| Parametric and polar | [Parametric curves](/learn/calculus-2/power-series-parametric-polar/parametric-curves) | [Polar coordinates](/learn/calculus-2/power-series-parametric-polar/polar-coordinates) |
| Vectors, dot and cross products | [The dot product](/learn/calculus-3/vectors-and-space/dot-product) | [Dot and cross product](/blog/vectors-dot-and-cross-product) |
| Curves and motion in space | [Curves and motion](/learn/calculus-3/vectors-and-space/curves-and-motion) | [Dot and cross product](/blog/vectors-dot-and-cross-product) |
| Partial derivatives and chain rule | [Partial derivatives](/learn/calculus-3/partial-derivatives/partial-derivatives) | [Partial derivatives](/blog/partial-derivatives) |
| Directional derivatives and gradient | [Gradient and directional derivatives](/learn/calculus-3/partial-derivatives/gradient-and-directional-derivatives) | [Gradient and directional derivatives](/blog/gradient-and-directional-derivatives) |

## MATH 1172 vs MATH 1152

| | MATH 1172 | MATH 1152 |
| --- | --- | --- |
| Title | Engineering Mathematics A | Calculus II |
| Credit hours | 5 | 5 |
| Series coverage | Divergence and ratio tests, Taylor series | All standard tests, power and Taylor series |
| Extra topics | Vectors, partial derivatives, gradient | Differential equations, polar calculus |
| Open to math majors | No | Yes |
| Next course | MATH 2153 | MATH 2153 |

You can take only one of the two. The [MATH 1152 guide](/courses/ohio-state-math-1152) covers the standard track, the [MATH 1151 guide](/courses/ohio-state-math-1151) reviews the prerequisite, and the [MATH 2153 guide](/courses/ohio-state-math-2153) 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:

$$\int x^2 e^x\,dx = x^2 e^x - 2\int x e^x\,dx = x^2 e^x - 2(x - 1)e^x + C = (x^2 - 2x + 2)e^x + C$$

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

$$e^{-x^2} = 1 - x^2 + \frac{x^4}{2} - \frac{x^6}{6} + \cdots$$

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

$$\nabla f = \langle 2xy,\ x^2 - 3y^2 \rangle = \langle 4, 1 \rangle$$

## 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](/learn/calculus-2/integration-techniques/techniques-practice) beat weekend cramming.
- **Learn the ratio test well.** It is the main convergence test in this course. The [ratio test page](/rules/ratio-test) 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](/practice) and the [formula sheet](/formulas) while learning.
- **Review** [common calculus mistakes](/blog/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.

## Frequently asked questions

### What is MATH 1172 at Ohio State?

MATH 1172, Engineering Mathematics A, is a 5-credit course that follows Calculus I. It covers techniques of integration, Taylor series and differential calculus of several variables, with applications.

### What is the difference between MATH 1172 and MATH 1152?

Both cover integration techniques and Taylor series. The department's topic list for 1172 uses only a few series tests and adds vectors, curves in space, partial derivatives and the gradient, while 1152 covers more series tests, differential equations and polar calculus. You can take only one of the two.

### Who can take MATH 1172?

Students with a C- or above in MATH 1151 or one of the other listed prerequisites. It is not open to math, pre-actuarial science or actuarial science majors, or to students who already have credit for MATH 1152.

### What comes after MATH 1172?

MATH 2153, Calculus III. MATH 1172 is one of its listed prerequisites.

### Is MATH 1172 hard?

It packs integration, series and a first look at multivariable calculus into one semester, so it moves quickly. Practicing a little every day keeps the topics from piling up.