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 Placement or 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 except for 18.024, for which one needs 18.014.
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 Alternatives
Two other flavors of 18.02 are 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.
18.023 Calculus II with Applications
Covers the material of 18.02 with an emphasis on applications. Additional material on asymptotic and numerical methods.
Advanced Placement and Credit for 18.01
A score of 4 or 5 on the Calculus BC exam gives you credit for 18.01. You may also receive credit for 18.01 by transferring credit from a comparable college course taken elsewhere, or by passing the Advanced Standing Exam administered by the Mathematics Department. If you have credit for 18.01, you may begin with 18.02, 18.022, or 18.023. If you have some calculus experience but not enough to get 18.01 credit, or wish to review the material even if you were given 18.01 credit, consider the 18.01A-18.02A sequence.
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 review of one-variable calculus, emphasizing integration techniques and applications, polar coordinates, improper integrals, and infinite series. Prerequisite is a score of 4 or 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 first 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 (57 units).
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: Freshmen are graded under Pass/Fail for 18.01A. If a freshman completes 18.02A during IAP, the grade is Pass/Fail. If a freshman completes 18.02A over Spring semester, the grade is ABC/NR.
18.014-18.024 Calculus with Theory
18.014 Fall only
18.024 Spring only
This version of the calculus sequence is intended for students with strong interest and ability in mathematics. Emphasis is placed on careful definitions of the concepts traditionally treated in calculus, and on mathematically rigorous proofs of the basic theorems of the subject. Students choosing 18.014 should already be familiar with the computational aspects of single-variable calculus. These aspects will, however, be reviewed when they arise during the term. The text by Apostol is used.
Credit Note: Students with 18.01 credit who decide to take 18.014 will lose the 12 units of 18.01 credit and instead receive nine units of general elective credit.