# Calculus

## Calculus — 2 Subjects, 12 Units Each

Mathematics is the common language of science and engineering, and calculus is a part of mathematics that is essential for understanding and describing many aspects of the physical world. The two-subject calculus General Institute Requirement (GIR) is designed to introduce the fundamental concepts of the calculus and provide the mathematical foundations on which subjects across MIT build.

The Mathematics GIR consists of 18.01 and 18.02 or equivalent courses. The 18.01 requirement can also be fulfilled by passing Advanced Standing exams or by transfer credit. 18.02 can be fulfilled by passing an Advanced Standing exam or by transfer credit.

Each of 18.01 and 18.02 is offered in several forms, with different course numbers. Any form of 18.01 credit fulfills the prerequisite for all forms of 18.02.

## Basic Sequence

The basic 18.01 - 18.02 calculus sequence is a traditional treatment adapted for MIT students. Both subjects are offered in both fall and spring. The approach is not rigorous; some theorems are proved carefully while others are justified informally.

### 18.01 Calculus I

Covers differentiation and integration of functions of one variable, with some basic applications. The prerequisites for 18.01 are high school algebra and trigonometry; any MIT student is eligible.

### 18.02 Calculus II

Covers vector and multi-variable calculus. Partial differentiation and multiple integration are studied with applications. Vectors, and vector-valued functions, and vector fields are introduced to describe physical notions such as velocity and force fields. Line and surface integrals are introduced along with their application to concepts of work and flux, and studied by means of the theorems of Green, Gauss, and Stokes.

## Fall 18.02 Alternative

Another flavor of 18.02 is offered in the Fall semester.

### 18.022 Calculus II

Covers the material of 18.02 with a more mathematical focus. Additional material is included on geometry, vector fields, and linear algebra.

## Advanced Placement and Credit for 18.01

You may receive credit for 18.01 three different ways: earning a score of 5 on the AP BC exam or comparable international exam (see: https://math.mit.edu/academics/undergrad/first/ap.php), transferring credit from a comparable college course taken elsewhere, or passing the Advanced Standing Exam administered by the Mathematics Department. If you have credit for 18.01, you may begin with 18.02 or 18.022. If you have some calculus experience but not enough to get 18.01 credit, or wish to review some of the material even if you were given 18.01 credit, consider the 18.01A-18.02A sequence.

## 18.0xA

### 18.01A-18.02A Calculus I and II

18.01A is given during the first six weeks of the Fall semester.

18.02A is begun during the second half of the Fall semester and completed during IAP or Spring
semester.

This sequence, intended for students who have had a full year of high school calculus, begins with 18.01A, a six-week class offering a very rapid review of one-variable calculus, focusing on the later topics of integration techniques and applications, polar coordinates, improper integrals, and infinite series. Prerequisite is a score of 5 on the Advanced Placement Calculus AB exam or a passing grade on the first half of the 18.01 Advanced Standing Exam, covering differentiation and elementary integration. Most students completing 18.01A continue directly into 18.02A, in which the remaining weeks of the fall term are devoted to the material in the first half of Calculus II. 18.02A is taught at the same pace as 18.02. Students complete the second half of Calculus II either during Independent Activities Period (IAP) in January or during the second half of the Spring term.

*Credit Notes:* Students opting for 18.01A-18.02A must register for both 18.01A and
18.02A in the Fall term, and for 18.02A in IAP or the Spring term. They receive 12 units of credit
upon completion of each subject, for a total of 24 units. Only 12 units (six for 18.01A and six
for 18.02A) are counted toward the Fall term credit limit (54 units). Depending on when the second
half of Calculus II is taken, six units will be applied toward the Independent Activities Period
credit limit (12 units) or the Spring term credit limit.

Students with 18.01 credit who decide to take 18.01A to review their calculus lose the 12 units of 18.01 credit but instead receive three units of general elective credit.

*Grading notes:* First-year students are graded under Pass/NoRecord for 18.01A. If the student completes 18.02A during IAP, the grade is Pass/NoRecord; if during Spring semester, the grade is ABC/NoRecord.