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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.

Cornell University Updated 3 min read

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
On this page
  1. What Cornell MATH 1910 covers
  2. MATH 1910 topic map
  3. The Cornell engineering sequence
  4. Example problems at the MATH 1910 level
  5. How to do well in MATH 1910

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 U-substitution
Integration by parts Integration by parts Integration by parts guide
Trig integrals and substitution Powers of sine and cosine Trig substitution
Partial fractions Partial fractions Partial fractions
Areas by integration Area between curves Area between curves
Volumes by integration Volumes with washers Volumes of revolution
Exponential growth Separable differential equations Natural exponential function
Sequences Sequences and their limits Limits at infinity
Tests of convergence Ratio and root tests Convergence tests, alternating series test
Power series Power series and radius Power series, 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 Second course Prerequisite MATH 1910 or equivalent
MATH 1120 Calculus II Non-engineering alternative to 1910 Forbidden overlap with MATH 1910

If your differentiation is rusty, work through the MATH 1110 guide 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

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.

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Integration by parts

Solve real problems on this topic with instant feedback, hints and a step-by-step walkthrough for every answer. Free, no sign-up needed to start.

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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.

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Related university courses

Cornell MATH 1920 Calculus 3 Multivariable Calculus for Engineers A study guide for Cornell MATH 1920 Multivariable Calculus for Engineers: partials, multiple integrals, line and surface integrals and Stokes, with practice. Cornell MATH 1120 Calculus 2 Calculus II A study guide for Cornell MATH 1120 Calculus II: integration techniques, improper integrals, differential equations and Taylor series, with practice. Cornell MATH 1110 Calculus 1 Calculus I A study guide for Cornell MATH 1110 Calculus I: limits, derivatives, the mean value theorem and the Fundamental Theorem, with practice for every topic.