# 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.

Source: https://practicecalculus.com/courses/mit-18-01a
Updated: 2026-11-03

## 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](/learn/calculus-2), with a [Calculus 1](/learn/calculus-1) refresher

## Key takeaways

- 18.01A is a six-week Calculus I subject held in the first half of the fall term.
- It assumes you already know how to differentiate and do elementary integrals, and spends its time on material beyond the AP AB syllabus.
- The core topics are integration techniques and their applications, improper integrals and infinite series.
- 18.01A and 18.01 exclude credit for each other, and both lead to a Calculus II subject such as 18.02.

**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](/courses/mit-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](/learn/calculus-1/integrals/fundamental-theorem-part-2) | [Fundamental Theorem of Calculus](/blog/fundamental-theorem-of-calculus) |
| 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 trig substitution | [Trig substitution](/learn/calculus-2/integration-techniques/trig-substitution) | [Trig substitution guide](/blog/trig-substitution) |
| Partial fractions | [Partial fractions](/learn/calculus-2/integration-techniques/partial-fractions) | [Partial fractions guide](/blog/partial-fractions) |
| Applications of integration | [Arc length and surface area](/learn/calculus-2/improper-integrals-and-applications/arc-length-and-surface-area) | [Volumes of revolution](/blog/volumes-of-revolution) |
| Improper integrals | [Integrating to infinity](/learn/calculus-2/improper-integrals-and-applications/infinite-limits-of-integration) | [Improper integrals](/blog/improper-integrals) |
| Infinite series and convergence | [The integral test and p-series](/learn/calculus-2/sequences-and-series/integral-test-and-p-series) | [Convergence tests](/blog/convergence-tests), [ratio test](/rules/ratio-test) |
| Power series and Taylor series | [Taylor polynomials](/learn/calculus-2/power-series-parametric-polar/taylor-polynomials) | [Taylor series](/blog/taylor-series), [power series](/blog/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](/courses/mit-18-02) or [18.022](/courses/mit-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](/rules/chain-rule). Run through the [Calculus 1 path](/learn/calculus-1) before term if anything feels rusty.
- **Learn to choose a technique, not just apply one.** The [choosing a strategy](/learn/calculus-2/integration-techniques/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](/rules/geometric-series-formula) or a p-series.
- **Keep the [formula sheet](/formulas) close** and test yourself with timed [practice exams](/practice) each week, since the midterm arrives fast.

> **Tip:** when a series test is inconclusive, check the [nth-term test](/rules/nth-term-test) first. If the terms do not go to zero, you are done.

## 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.