# Cornell MATH 1910 Calculus for Engineers: Study Guide and Practice

> A study guide for Cornell MATH 1910 Calculus for Engineers: integration techniques, areas and volumes, partial fractions and power series, with practice.

Source: https://practicecalculus.com/courses/cornell-math-1910
Updated: 2026-11-03

## At a glance

- **Course code:** MATH 1910
- **Credits:** 4
- **Recently offered:** Fall, spring and summer
- **Assumes:** Differential calculus at the level of MATH 1110
- **Covers:** Techniques of integration, areas and volumes, exponential growth, partial fractions, infinite sequences and series, convergence tests, power series
- **Forbidden overlap:** MATH 1120 Calculus II
- **Next course:** MATH 1920 Multivariable Calculus for Engineers
- **Practice here:** [Calculus 2](/learn/calculus-2)

## Key takeaways

- MATH 1910 is the first course in Cornell's engineering math sequence and is essentially a second course in calculus.
- It assumes differential calculus at the level of MATH 1110 and focuses on integration and series.
- Topics include integration techniques, areas and volumes, exponential growth, partial fractions, sequences and series, convergence tests and power series.
- It is followed by MATH 1920, and it excludes credit for MATH 1120.

**Cornell MATH 1910**, Calculus for Engineers, is the first math course most Cornell engineering students take. Despite the number, it is essentially a second course in calculus: it assumes you already know differential calculus at the MATH 1110 level and moves straight into integration and series. This guide maps each MATH 1910 topic to a lesson you can practice with instant feedback.

## What Cornell MATH 1910 covers

The Cornell class roster describes MATH 1910 as the first course in a sequence designed for engineers. Topics include techniques of integration, finding areas and volumes by integration, exponential growth, partial fractions, infinite sequences and series, tests of convergence, and power series.

In standard terms that is a **Calculus 2** course. It overlaps closely with the integration techniques, applications, and sequences and series units of the Calculus 2 path on PracticeCalculus.

## MATH 1910 topic map

| MATH 1910 topic | Practice | Read |
| --- | --- | --- |
| Review: u-substitution | [U-substitution refresher](/learn/calculus-2/integration-techniques/u-substitution-refresher) | [U-substitution](/blog/u-substitution) |
| Integration by parts | [Integration by parts](/learn/calculus-2/integration-techniques/integration-by-parts) | [Integration by parts guide](/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) |
| Areas by integration | [Area between curves](/learn/calculus-1/applications-of-integrals/area-between-curves) | [Area between curves](/blog/area-between-curves) |
| Volumes by integration | [Volumes with washers](/learn/calculus-1/applications-of-integrals/volumes-washers) | [Volumes of revolution](/blog/volumes-of-revolution) |
| Exponential growth | [Separable differential equations](/learn/calculus-2/improper-integrals-and-applications/separable-equations) | [Natural exponential function](/functions/natural-exponential-function) |
| Sequences | [Sequences and their limits](/learn/calculus-2/sequences-and-series/sequences) | [Limits at infinity](/blog/limits-at-infinity) |
| Tests of convergence | [Ratio and root tests](/learn/calculus-2/sequences-and-series/ratio-and-root-tests) | [Convergence tests](/blog/convergence-tests), [alternating series test](/rules/alternating-series-test) |
| Power series | [Power series and radius](/learn/calculus-2/power-series-parametric-polar/power-series-and-radius) | [Power series](/blog/power-series), [Taylor series](/blog/taylor-series) |

## The Cornell engineering sequence

| Course | Role | Notes from the roster |
| --- | --- | --- |
| MATH 1910 Calculus for Engineers | First course in the engineering sequence | Assumes MATH 1110 level differential calculus |
| [MATH 1920 Multivariable Calculus for Engineers](/courses/cornell-math-1920) | Second course | Prerequisite MATH 1910 or equivalent |
| [MATH 1120 Calculus II](/courses/cornell-math-1120) | Non-engineering alternative to 1910 | Forbidden overlap with MATH 1910 |

If your differentiation is rusty, work through the [MATH 1110 guide](/courses/cornell-math-1110) topics first, especially the chain rule and inverse trig derivatives.

## Example problems at the MATH 1910 level

**1. Partial fractions.** Since $\frac{1}{x^2 - 1} = \frac{1}{2}\left(\frac{1}{x - 1} - \frac{1}{x + 1}\right)$,

$$\int \frac{dx}{x^2 - 1} = \frac{1}{2}\ln\left|\frac{x - 1}{x + 1}\right| + C$$

**2. A volume of revolution.** Rotate $y = \sqrt{x}$, $0 \le x \le 4$, about the $x$-axis. By disks,

$$V = \pi \int_0^4 (\sqrt{x})^2\,dx = \pi \int_0^4 x\,dx = \pi \left[\frac{x^2}{2}\right]_0^4 = 8\pi$$

**3. The ratio test.** For $\sum_{n=1}^{\infty} \frac{n}{2^n}$:

$$\lim_{n \to \infty} \frac{n + 1}{2^{n+1}} \cdot \frac{2^n}{n} = \lim_{n \to \infty} \frac{n + 1}{2n} = \frac{1}{2} < 1$$

so the series converges.

## How to do well in MATH 1910

- **Shore up differentiation in week one.** The course assumes it. Run through [mixed rules practice](/learn/calculus-1/derivative-rules/derivative-rules-practice) and the [derivative rules recap](/learn/calculus-1/derivative-rules/derivative-rules-summary).
- **Draw the slice for every volume.** Decide disk or washer from the picture, then write the radius. Most volume errors are a wrong radius.
- **Learn convergence tests as a decision process.** Our [convergence tests guide](/blog/convergence-tests) and the [choosing a test](/learn/calculus-2/sequences-and-series/choosing-a-test) lesson make the order of attack routine.
- **Keep the [formula sheet](/formulas) at hand**, study [common calculus mistakes](/blog/common-calculus-mistakes), and test yourself with [practice exams](/practice) before prelims.

> **Tip:** exponential growth problems almost always reduce to $y = y_0 e^{kt}$. Find $k$ from one data point, then answer the question with the other.

## Frequently asked questions

### What is Cornell MATH 1910?

MATH 1910 Calculus for Engineers is a 4-credit course that is essentially a second course in calculus. It covers techniques of integration, areas and volumes, exponential growth, partial fractions, infinite sequences and series, convergence tests and power series.

### Do I need MATH 1110 before MATH 1910?

The roster says MATH 1910 assumes familiarity with differential calculus at the level of MATH 1110. Many engineering students meet that with high school calculus, but you should be comfortable with limits, derivative rules and basic integrals before starting.

### Is MATH 1910 the same as MATH 1120?

They cover very similar single-variable material, and credit is given for only one. MATH 1910 is designed for engineers and leads into MATH 1920, the engineering multivariable course.

### What comes after MATH 1910?

MATH 1920 Multivariable Calculus for Engineers, which lists MATH 1910 or equivalent as its prerequisite.

### Is MATH 1910 hard?

It starts at Calculus 2, so there is little review of differentiation, and series can feel abstract at first. Students who keep integration techniques sharp with daily practice tend to handle it well.