practicecalculus
Log in Start free
MIT

MIT 18.01A Calculus: Topics, Study Guide and Practice

A study guide for MIT 18.01A, the six-week Calculus I review: integration techniques, improper integrals and series, mapped to free practice.

MIT Updated 3 min read

At a glance

Course code
18.01A (Calculus, satisfies the Calculus I GIR)
Units
5-0-7 (12 units)
Offered
Fall, first half of term
Prerequisites
Knowledge of differentiation and elementary integration
Covers
A fast review of one-variable calculus focused on what the AP AB syllabus leaves out: integration techniques and applications, improper integrals and infinite series
Next course
18.02, 18.02A or 18.022 (Calculus II, multivariable)
Practice here
Calculus 2, with a Calculus 1 refresher
On this page
  1. What MIT 18.01A covers
  2. 18.01A topic map
  3. 18.01A vs 18.01
  4. Example problems at the 18.01A level
  5. How to do well in MIT 18.01A

MIT 18.01A is the fast track through Calculus I at MIT. It runs for only the first six weeks of the fall term and is meant for students who arrive already knowing how to differentiate and integrate basic functions, typically from a high school calculus course. Instead of re-teaching derivatives, it concentrates on the parts of single-variable calculus that an AB-level course does not reach. This guide maps each topic to free practice.

What MIT 18.01A covers

The MIT catalog calls 18.01A a six-week review of one-variable calculus that emphasizes material not on the high school AB syllabus. That means integration techniques and their applications, improper integrals, and infinite series, plus applications to other areas such as probability and statistics when time allows. It satisfies the same Calculus I requirement as 18.01, and the two exclude credit for each other.

Measured against a standard sequence, 18.01A is mostly Calculus 2 material: the integration techniques unit, improper integrals and the series unit, with a quick review of the Calculus 1 ideas they rest on.

18.01A topic map

18.01A topic Practice Read
Review: derivatives and basic integrals Evaluating definite integrals Fundamental Theorem of Calculus
Substitution U-substitution refresher U-substitution
Integration by parts Integration by parts Integration by parts guide
Trig integrals and trig substitution Trig substitution Trig substitution guide
Partial fractions Partial fractions Partial fractions guide
Applications of integration Arc length and surface area Volumes of revolution
Improper integrals Integrating to infinity Improper integrals
Infinite series and convergence The integral test and p-series Convergence tests, ratio test
Power series and Taylor series Taylor polynomials Taylor series, power series

18.01A vs 18.01

Subject Prerequisite Length Focus
18.01 None Full semester, fall or spring All of single-variable calculus from limits to series
18.01A Differentiation and elementary integration First six weeks of fall Integration techniques, improper integrals, series
18.02A Calculus I Starts in the last six weeks of fall First half of multivariable calculus

Because 18.01A ends at mid-semester, the calendar lines up with 18.02A, whose first half runs in the second half of fall. You can also take 18.02 or 18.022 in a later term.

Example problems at the 18.01A level

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

\int \frac{dx}{x(x+1)} = \ln|x| - \ln|x+1| + C = \ln\left|\frac{x}{x+1}\right| + C

2. A divergent improper integral.

\int_1^{\infty} \frac{dx}{x} = \lim_{t\to\infty} \ln t = \infty

so the integral diverges, while \int_1^\infty x^{-2}\,dx = 1 converges. The exponent 1 is the dividing line.

3. A geometric series.

\sum_{n=0}^{\infty} \frac{2}{3^n} = \frac{2}{1 - \frac{1}{3}} = 3

How to do well in MIT 18.01A

  • Arrive with Calculus 1 automatic. Six weeks leaves no time to relearn the chain rule. Run through the Calculus 1 path before term if anything feels rusty.
  • Learn to choose a technique, not just apply one. The choosing a strategy lesson trains the decision that exams test.
  • Anchor series on two families. Almost every comparison goes back to the geometric series formula or a p-series.
  • Keep the formula sheet close and test yourself with timed practice exams each week, since the midterm arrives fast.

Tip: when a series test is inconclusive, check the nth-term test first. If the terms do not go to zero, you are done.

Practice it now

U-substitution refresher

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.

Practice this lesson

Frequently asked questions

What is MIT 18.01A?
18.01A is a six-week review of single-variable calculus that runs in the first half of the fall term. It satisfies the Calculus I requirement and focuses on integration techniques, improper integrals and infinite series, with other applications such as probability and statistics if time allows.

Should I take 18.01 or 18.01A?
The catalog lists knowledge of differentiation and elementary integration as the prerequisite for 18.01A. If derivatives, basic antiderivatives and the Fundamental Theorem already feel routine, 18.01A fits. If not, the full-semester 18.01 builds those skills from the start.

What comes after 18.01A?
A Calculus II subject: 18.02, 18.02A or 18.022. The first half of 18.02A is taught in the last six weeks of fall, so it follows directly on the calendar.

Is 18.01A hard?
The pace is the main challenge, since it covers a large share of a typical Calculus 2 course in six weeks. A solid AP-level background and daily practice make it manageable.

How do I prepare for 18.01A?
Review derivative rules, u-substitution and definite integrals until they are automatic, then preview integration by parts and geometric series. Practicing those before the term starts means you can focus on the new material.

Written by the PracticeCalculus team

We build interactive calculus lessons and write every page to be clear and correct. Spotted something off? Tell us and we will fix it.

Related university courses

MIT 18.01 Calculus 1 and 2 Single Variable Calculus A study guide for MIT 18.01 (Calculus I): every topic it covers, from derivatives to power series, how it compares to 18.01A and 18.02, and where to practice. MIT 18.02 Calculus 3 Calculus A study guide for MIT 18.02 (Calculus II): vectors, partial derivatives, multiple integrals and the theorems of Green and Stokes, mapped to free practice. MIT 18.022 Calculus 3 Calculus A study guide for MIT 18.022, the concept-focused Calculus II: vectors, matrices, curvature, vector fields, multiple integrals and Stokes, with free practice.