Department of Mathematics at MIT | Undergraduate Study: 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 many aspects of the physical world. The two-subject calculus requirement can be fulfilled through various sequences or a combination of subjects and Advanced Placement or Advanced Standing credit, depending on your mathematics background and interests. The basic 18.01-18.02 calculus sequence is a traditional treatment adapted for MIT students. Both subjects are offered in the 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. 18.02 Calculus II Covers vector and multi-variable calculus. Partial differentiation and multiple integration are studied with applications. Vectors and vector functions are introduced to describe physical notions such as work and force field. Line and surface integrals are covered along with the theorems of Green, Gauss, and Stokes, which are fundamental in many problems of physics and engineering. A variant of 18.02 is described below. It is only offered in the fall term. 18.022 Calculus II Covers the material of 18.02, but at greater depth. Additional material is included in geometry, vector fields, and linear algebra. Advanced Placement and Credit 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 an advanced standing exam. 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 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 Fall only (six weeks) 18.02A Fall, plus IAP or Spring 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 will continue directly into 18.02A, in which the remaining weeks of the fall term will be devoted to the material in the first half of Calculus II. 18.02A will be taught at the same pace as 18.02. Students will then 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 will register for both 18.01A and 18.02A in the fall term, and for 18.02A in IAP or the spring term. They will 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) will be 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 will lose the 12 units of 18.01 credit and instead receive three units of general elective credit. 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. Advice for Choosing Your Fall Term Calculus Subject If you have had less than a full year of calculus in high school, enroll in 18.01. If you have had a full year of calculus but do not have 18.01 credit, take the 18.01 Advanced Standing Examination. Passing the first part gives eligibility for 18.01A. Passing both parts gives 18.01 credit. If you have 18.01 credit, you may choose between 18.02 and 18.022. If you wish a review, you may take 18.01A. If you are especially interested in mathematics and have some prior calculus experience, consider 18.014. All calculus lectures are scheduled at the same time to facilitate switching to another sequence if the one you choose isn't suitable. However, with the exception of 18.01 and 18.01A, each subject sequence uses a different book, so some catching up would be necessary.