18.022 | Fall 2010 | Undergraduate

Calculus of Several Variables

Instructor Insights

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


Calculus I GIR

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

Requirements Satisfied

Calculus II GIR


Every fall semester


The students’ grades were based on the following activities:

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

Student Information


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:


  • 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.


  • 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

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

Course Info

As Taught In
Fall 2010
Learning Resource Types
Problem Sets with Solutions
Exams with Solutions
Lecture Notes
Instructor Insights