### Course Overview

This page focuses on the course *18.022 Calculus of Several Variables* as it was taught by Prof. James McKernan in Fall 2010.

This is a course in multivariable calculus, with more focus on mathematical concepts than *18.02 Multivariable Calculus*.

### Course Outcomes

#### Course Goals for Students

The students will learn about vectors, dot products, cross products, how to describe lines and planes, functions of more than one variable, parameterizations of curves and surfaces, partial derivatives, iterated integrals, gradient, divergence and curl, Green’s Theorem, Stokes’ Theorem, and the divergence theorem.

### Curriculum Information

#### Prerequisites

Calculus I GIR

Any of the following courses at MIT will prepare you for 18.022:

*18.01 Calculus**18.014 Calculus with Theory**18.01A Calculus**CC.181A Calculus**ES.1801 Calculus**ES.181A Calculus*

#### Requirements Satisfied

Calculus II GIR

#### Offered

Every fall semester

### Assessment

The students’ grades were based on the following activities:

- 25% Assignments
- 45% Hour Exams; 3 exams at 15% each
- 30% Final Exam

### Student Information

#### Enrollment

83 students

#### Breakdown by Year

This is intended mainly as a course for freshmen.

#### Typical Student Background

- Most MIT students will take 18.02, which emphasizes applications of calculus to the sciences (especially physics).
- This course, 18.022, is geared to students who have a more theoretical interest in multivariable calculus, perhaps because they are interested in majoring in mathematics.
- Some students may have seen calculus in high school and want to take a more challenging class.

### How Student Time Was Spent

During an average week, students were expected to spend 12 hours on the course, roughly divided as follows:

#### Lecture

- Met 3 times per week for 1 hour per session; 37 sessions total.
- The final exam was held during Finals Week in one 3-hour session.

#### Recitation

- Met 2 times per week for 1 hour per session; 26 sessions total.
- Students chose 1 of 4 scheduled times to attend; ~20 students in each section.
- Led by the teaching assistants.

#### Out of Class

- Complete the problem sets.
- Study for the exams.

### Course Team Roles

#### Lead Instructor (Prof. James McKernan)

- The lead instructor developed the course material, structured the course, and delivered the lectures

#### Teaching Assistants

- This course had four teaching assistants
- Each teaching assistant led 1/4 of the students in a recitation section; each section met twice a week for 1 hour each session
- The teaching assistants graded the problem sets and the exams