Instructor Insights

Instructor Insights pages are part of the OCW Educator initiative, which seeks to enhance the value of OCW for educators.

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:

Requirements Satisfied

Calculus II GIR

Offered

Every fall semester

The Classroom

  • A large classroom with tiered seating and several chalkboards.

    Room 1 of 3 Click for next classroom.

    Lecture

    The lectures were held in this large classroom with chalkboards.

  • A classroom with tables and chairs for 30 students.

    Click for previous classroom. Room 2 of 3

    Recitation

    The recitations were held in this smaller classroom.

  • A large room with separate tables and chairs for every student.

    Room 3 of 3 Click for next classroom.

    Exam

    Exams were administered in this large room.

 

Assessment

The students' grades were based on the following activities:

The color used on the preceding chart which represents the percentage of the total grade contributed by midterm exams. 45% Hour Exams; 3 exams at 15% each
 

Student Information

83 students took this course in Fall 2010.

Enrollment

This course is significantly smaller than 18.02, which usually has close to 500 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

3 hours per week
  • 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

2 hours per week
  • 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

7 hours per week
 

Semester Breakdown

WEEK M T W Th F
1 No classes throughout MIT. No classes throughout MIT. Recitation scheduled. Lecture session scheduled. Lecture session scheduled.
2 Recitation scheduled. Lecture session scheduled. Recitation scheduled. Lecture session scheduled; assignment due date. Lecture session scheduled.
3 Recitation scheduled. Lecture session scheduled. Recitation scheduled. Lecture session scheduled; assignment due date. Lecture session scheduled.
4 Recitation scheduled. Lecture session scheduled; exam held. Recitation scheduled. Lecture session scheduled; assignment due date. Lecture session scheduled.
5 Recitation scheduled. Lecture session scheduled. Recitation scheduled. Lecture session scheduled; assignment due date. Lecture session scheduled.
6 No classes throughout MIT. Lecture session scheduled. Recitation scheduled. Lecture session scheduled; assignment due date. Lecture session scheduled.
7 Recitation scheduled. Lecture session scheduled. Recitation scheduled. Lecture session scheduled; assignment due date. Lecture session scheduled; exam held.
8 Recitation scheduled. Lecture session scheduled. Recitation scheduled. Lecture session scheduled; assignment due date. Lecture session scheduled.
9 Recitation scheduled. Lecture session scheduled. Recitation scheduled. Lecture session scheduled; assignment due date. Lecture session scheduled.
10 Recitation scheduled. Lecture session scheduled. Recitation scheduled; assignment due date. No classes throughout MIT. Lecture session scheduled; exam held.
11 Recitation scheduled. Lecture session scheduled. Recitation scheduled. Lecture session scheduled; assignment due date. Lecture session scheduled.
12 Recitation scheduled. Lecture session scheduled. Recitation scheduled. No classes throughout MIT. No classes throughout MIT.
13 Recitation scheduled. Lecture session scheduled. Recitation scheduled. Lecture session scheduled; assignment due date. Lecture session scheduled.
14 Recitation scheduled. Lecture session scheduled. Recitation scheduled. Lecture session scheduled; assignment due date. No classes throughout MIT.
15 No classes throughout MIT. No classes throughout MIT; final exam held. No classes throughout MIT. No classes throughout MIT. No classes throughout MIT.
Displays the color and pattern used on the preceding table to indicate dates when classes are not held at MIT. No classes throughout MIT
Displays the color used on the preceding table to indicate dates when lecture sessions are held. Lecture session
Displays the symbol used on the preceding table to indicate dates when assignments are due. Assignment due date
Displays the color used on the preceding table to indicate dates when no class session is scheduled. No class session scheduled
Displays the color used on the preceding table to indicate dates when recitations are held. Recitation
Displays the symbol used on the preceding table to indicate dates when exams are held. Exam
 

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