# MIT 18.01 Single Variable Calculus: Topics, Study Guide, Practice

> 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.

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

## At a glance

- **Course code:** 18.01 (listed in the catalog as Calculus, the Calculus I GIR)
- **Units:** 5-0-7 (12 units)
- **Offered:** Fall and spring
- **Prerequisites:** None
- **Covers:** Differentiation, integration, techniques of integration, polar coordinates, L'Hôpital's rule, improper integrals, infinite and power series
- **Next course:** 18.02, 18.02A or 18.022 (Calculus II, multivariable)
- **Practice here:** [Calculus 1](/learn/calculus-1) plus the first units of [Calculus 2](/learn/calculus-2)

## Key takeaways

- MIT 18.01 is a one-semester course in single-variable calculus with no prerequisites, offered every fall and spring.
- It covers what many universities split across Calculus 1 and the start of Calculus 2: derivatives, integrals, integration techniques, improper integrals and series.
- 18.01A is a faster six-week version for students who already know basic differentiation and integration.
- After 18.01, students take a Calculus II subject: 18.02, 18.02A or 18.022.

**MIT 18.01** is MIT's first-semester calculus subject, part of the Calculus I General Institute Requirement. It covers single-variable calculus from the first derivative to power series in one term, which is more ground than most Calculus 1 courses elsewhere. This guide maps every 18.01 topic to free practice, so you can learn each idea by solving problems with instant feedback.

## What MIT 18.01 covers

According to the MIT course catalog, 18.01 covers differentiation and integration of functions of one variable, with applications to geometry and science. It then goes further than a typical Calculus 1 course, adding techniques of integration, polar coordinates, L'Hôpital's rule, improper integrals, and infinite series including power series.

In practice, that means 18.01 spans two courses at many other universities: all of **Calculus 1** and the first half of **Calculus 2**.

## 18.01 topic map

Each row links to a lesson you can practice and to a reference page or guide that explains the idea.

| 18.01 topic | Practice | Read |
| --- | --- | --- |
| Limits and continuity | [Limits](/learn/calculus-1/limits/what-is-a-limit) | [What is a limit?](/blog/what-is-a-limit) |
| The derivative | [The limit definition](/learn/calculus-1/the-derivative/limit-definition) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| Differentiation rules | [Power rule](/learn/calculus-1/derivative-rules/power-rule) | [Chain rule](/rules/chain-rule), [product rule](/rules/product-rule) |
| Applications of derivatives | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Optimization problems](/blog/optimization-problems), [related rates](/blog/related-rates) |
| The definite integral | [Riemann sums](/learn/calculus-1/integrals/riemann-sums) | [Fundamental Theorem of Calculus](/theorems/fundamental-theorem-of-calculus-part-2) |
| Applications of integration | [Area between curves](/learn/calculus-1/applications-of-integrals/area-between-curves) | [Volumes of revolution](/blog/volumes-of-revolution) |
| Techniques of integration | [Integration by parts](/learn/calculus-2/integration-techniques/integration-by-parts) | [u-substitution](/blog/u-substitution), [partial fractions](/blog/partial-fractions) |
| L'Hôpital's rule | [L'Hôpital's rule](/learn/calculus-1/applications-of-derivatives/lhopitals-rule) | [L'Hôpital's rule](/rules/lhopitals-rule) |
| Improper integrals | [Integrating to infinity](/learn/calculus-2/improper-integrals-and-applications/infinite-limits-of-integration) | [Improper integrals](/blog/improper-integrals) |
| Infinite and power series | [Geometric series](/learn/calculus-2/sequences-and-series/geometric-series) | [Convergence tests](/blog/convergence-tests), [Taylor series](/blog/taylor-series) |
| Polar coordinates | [Power series, parametric and polar](/learn/calculus-2/power-series-parametric-polar/power-series-and-radius) | [Power series](/blog/power-series) |

## 18.01 vs 18.01A vs 18.02

| Subject | Who it is for | Pace |
| --- | --- | --- |
| 18.01 | Students starting single-variable calculus | Full semester |
| 18.01A | Students who already know differentiation and basic integration | First six weeks of fall |
| 18.02 | Students who have finished Calculus I | Full semester, multivariable |

18.01 and 18.01A both satisfy Calculus I and exclude credit for each other. If you took a strong high school calculus course, 18.01A lets you spend most of your time on integration techniques, improper integrals and series. See the [MIT 18.02 guide](/courses/mit-18-02) for what comes next.

## Example problems at the 18.01 level

These three problems show the range of the course, from a first derivative to a series.

**1. A chain rule derivative.** Differentiate $y = \sin(x^2)$.

$$\frac{dy}{dx} = \cos(x^2) \cdot 2x = 2x\cos(x^2)$$

**2. Integration by parts.** Evaluate $\int x e^x\,dx$ with $u = x$ and $dv = e^x\,dx$:

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

**3. A convergent improper integral.**

$$\int_1^{\infty} \frac{1}{x^2}\,dx = \lim_{t \to \infty}\left[-\frac{1}{x}\right]_1^t = \lim_{t \to \infty}\left(1 - \frac{1}{t}\right) = 1$$

## How to do well in MIT 18.01

- **Practice every day in short sessions.** The course covers a lot in one term, and skills like the [chain rule](/rules/chain-rule) only become automatic through repetition.
- **Fix algebra slips early.** Most lost points come from algebra and sign errors, not calculus. Our list of [common calculus mistakes](/blog/common-calculus-mistakes) covers the big ones.
- **Keep the formulas in front of you.** The [calculus formula sheet](/formulas) has every derivative and integral on one page.
- **Test yourself under time pressure** before each exam, using [practice exams](/practice) with fresh numbers every time.

> **Tip:** if series feel abstract at first, start with the [geometric series formula](/rules/geometric-series-formula). Almost every convergence argument in 18.01 builds on it.

## Frequently asked questions

### What is MIT 18.01?

MIT 18.01 is the Institute's Calculus I subject: single-variable differentiation and integration with applications, techniques of integration, polar coordinates, L'Hôpital's rule, improper integrals and infinite series.

### What is the difference between 18.01 and 18.01A?

18.01A is a six-week review in the first half of the fall term for students who already know differentiation and elementary integration. It concentrates on integration techniques, improper integrals and series. The two subjects exclude credit for each other.

### What comes after MIT 18.01?

The next subject is Calculus II, which is multivariable calculus: 18.02, the split 18.02A, or the more theoretical 18.022.

### Is MIT 18.01 hard?

It moves fast, because it fits a full Calculus 1 course plus integration techniques and series into one semester. Students who practice a little every day, rather than cramming before exams, find it much more manageable.

### How can I prepare for 18.01?

Make sure your algebra, exponent rules and trig values are solid, then work through limits and derivatives with lots of short practice problems. The free Calculus 1 path on PracticeCalculus follows the same order.