Fall 2019 Multivariable Calculus
Math 18.02, Concourse - MIT
Fall 2019

Lectures and Recitations by:
Robert Winters
Robert@math.rwinters.com

Calendar of topics and
homework assignments
Solutions

Concourse 18.02 Stellar site


(former) Concourse 18.03 site

(former) Concourse 18.02 site

(former) Concourse 18.01A-02A site


Torus

The text for the course is
Multivariable Calculus, 6th Edition by Edwards & Penney (ISBN 0130339679 for softcover edition)
[Click on the image below for prices.]

"Calculus: Multivariable" by McCallum, Hughes-Hallett, Gleason, et al.

Table of Contents:

• Ch. 12 - Vectors, Curves, and Surfaces in Space

• Ch. 13 - Partial Differentiation

• Ch. 14 - Multiple Integrals

• Ch. 15 - Vector Calculus

This is the site of the Concourse 18.02 course (a.k.a. CC.1802) that ran for 9 years from Fall 2011 through Fall 2019. I imagine that some version of the course will continue within the remnants of the Concourse Program, a program that billed itself as “integrating science and the humanities” but which made no effort to actually do so for at least the last 8 years. Concourse has sold that false bill of goods simply to justify its continued existence as an MIT Freshman Learning Community.

The students of Concourse are much the same as virtually all MIT students - curious, smart, and a pleasure to know. The Concourse Program, in contrast, is built on a foundation of hypocrisy. Themes like justice and truth and knowledge are presented to its students, but what has come to define Concourse are the need for control and enforcing obedience and taking care of the selfish needs of the administrators of the program. Those of us who were simply very good at teaching our courses (and greatly appreciated by our students) and who did our best to actually integrate science and the humanities or, in my case, civic responsibility, have never been valued by the directors of the program. Those who teach in Concourse actually have very little say in how the program operates, and the program has largely been on auto-pilot for some time. That said, you could probably randomly pick 50 MIT freshmen and make it work as long as good teachers were in the program who actively engaged students.

I treasure all of my relationships with students built up over 9 years working in Concourse as well as the absolute joy of sharing an office for most of my time there with a truly wonderful teacher of Chemistry and mentor of students. I miss the students more than I can put into words. However, I don’t at all miss working an an oppressive environment with an incompetent and vengeful Assistant Director and a Director who values only blind obedience and who would gladly throw under the bus anyone whose independence in any way threatened her personal insecurities. Any academic program, including any MIT Freshman Learning Community, should aspire to greater things. - Robert Winters

Announcements:

A variant of this course is now offered at the Harvard University Extension School (Math E-21a).
email: robert@math.rwinters.com


Syllabus for Concourse Math 18.02     Printable syllabus (PDF)

Topics and Assignments are posted in the Course Calendar.

Lecture times: Mon, Wed 3:00pm-4:30pm 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


Mathlet (Java applet) for Curves and Surfaces (may be helpful for P-sets)

Text: Multivariable Calculus, 6th Edition by Edwards & Penney (ISBN 0130339679 for softcover edition).

Supplementary Notes: 18.02 Notes authored by Prof. Arthur Mattuck of the MIT Mathematics Department.

Mega-List of Math 18.02 techniques     Math 18.02 Useful Facts


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

Text: Multivariable Calculus, 6th Edition by Edwards & Penney (ISBN 0130339679 for softcover edition).


Singular Sensations - Steve Strogatz in the New York Times


Supplementary Notes: 18.02 Notes authored by Prof. Arthur Mattuck of the MIT Mathematics Department.

Homework: Homework will be posted on the course website and will be due approximately weekly. Typical assignments will include some exercises that are to be turned in as well as additional practice problems. Homework may be submitted in class or at my office, but it should be completed by the posted due date. Additional time will only be given if requested before the due date and if appropriate for the circumstances. You should not consult any solutions manual 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.


Topics and Assignments are posted in the Course Calendar.

Mathlet (Java applet) for Curves and Surfaces (may be helpful for P-sets)


You can contact me at either robert@math.rwinters.com or Robert@rwinters.com.


Here's something:  http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/index.html


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Please send comments to Robert Winters.
URL: http://math.rwinters.com/1802
Last modified: Tuesday, January 3, 2023 10:28 AM