Math 18.02 - Concourse: Multivariable Calculus - Fall 2019

Lectures and Recitations by: Robert Winters
Office: 16-137 and Concourse Lounge
Office phone: x3-2050 (e-mail is better)
E-mail address:

Lecture times: Mon, Wed 12:00am-1:30pm in 16-160

Recitation times: Tues, Thurs 12:00-1:00pm in 16-160

Office hours: Tues, Thurs 2:00-3:00pm and at other times to be determined


Prerequisites: Math 18.01 or equivalent (one-variable Calculus).

Texts: Multivariable Calculus, 6th Edition by Edwards & Penney (ISBN 0130339679). Also, we'll be drawing from the 18.02 Notes & Exercises authored by Prof. Arthur Mattuck in the MIT Mathematics Department and developed over many years. These will be available as downloadable PDF files.

Website: Homework assignments, solutions, supplements, and anything that needs posting for the course will be found at this website. We will also have a Stellar site for other administrative matters as well as a link to the active website.

Homework: Homework will be posted on the course website and will be due approximately weekly. Exact due dates will be indicated in the Course Calendar accessible from the website. Typical assignments will include some exercises that are to be turned in as well as additional practice problems. Some of the exercises will be drawn from the text(s), but a typical problem set will contain both text exercises plus additional exercises. Intersecting cylindersHomework may be submitted in class or at my office, but it should be completed by the posted due date. You should not consult any solutions manual or similar sources in preparing your assignments. You are encouraged to work with your fellow students on the homework, but your written solutions must be your own. Solutions will be made available (as PDF files) on the course website shortly after they are due.

Exams: We anticipate 3 midterm exams (tentatively Sept 30, Oct 28, and Nov 25). There will also be a Final Exam.

Grading: (This scheme may be adjusted slightly)
Homework assignments 30%
Midterm exams 40% (we anticipate assigning less weight to your lowest exam score)
Final exam 30%

Condensed Syllabus: (See the Calendar for day-by-day details, updated as the course proceeds.)

Multivariable Calculus
The text for the course is
Multivariable Calculus
6th edition
by Edwards & Penney
ISBN 0130339679 for softcover edition

  • Vectors and vector algebra in R2 and R3; dot product, cross product, projection, equations of lines and planes. Matrix methods.(Chap. 12)
  • Parameterized curves and surfaces in R2 and R3; velocity and acceleration vectors; tangent vectors; arclength. (Chap. 12)
  • Functions of several variables - limits, continuity, and differentiabilty; partial derivatives, gradients, linear approximation, directional derivatives, Chain Rule. (Chap. 13)
  • Optimization - unconstrained and constrained. (Chap. 13)
  • Integration over regions in R2 and R3 and their applications, using Cartesian, polar, cylindrical, and spherical coordinates. (Chap. 14)
  • Vector fields and their applications. (Chap. 15)
  • Integration over curves in R2 and R3 by parameterization; work integrals, and applications. (Chap. 15)
  • Integration over surfaces in R3 by parameterization - flux integrals, surface area, and applications. (Chaps. 14, 15)
  • Calculus of vector fields; curl and divergence of vector fields; Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem. (Chap. 15)