Fall 2011
Multivariable Calculus
Math 18.02, Concourse - MIT

Lectures by: Robert Winters
rwinters@mit.edu
Office: 16-137
Phone: x3-2050
(but e-mail is better)

Recitations by: Lucas Culler
luccul@math.mit.edu
Office: 2-587
Phone: x3-4129

Calendar of topics and
homework assignments
Solutions
(username/password required)

Concourse Stellar site

 

Concourse 18.02 Stellar 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

Announcements:

Problem Set #10 is now posted but is not to be turned in. It covers the last topics of the course, including Stokes' Theorem.

Detailed Problem Set #10

The Final Exam took place on Tuesday, December 20 from 9:00am to noon in 16-160.

A practice Final Exam from 2010 (with solutions) and an actual Final Exam from 2010 (with solutions) are posted on the Solutions Page. These are the same exams posted on the Open Courseware site under 18.02SC.


Exam #4 took place during the latter part of class on Thursday, Dec 8. Topics included integration of functions over curves and surfaces (line and surface integrals) with applications to mass, averaging, centroids, flux, etc.; flux integrals in 2- and 3-dimensions; conservative vector fields and potential functions; Fundamental Theorem of Line Integrals, Green's Theorem, Divergence Theorem.


Approximate letter grades for Exam #1
Total points on exam was 54. Median score was 47.
Mean score was 46.2. Standard deviation was 4.3.
score grade   score grade
50+ A 35+ C+
47+ A– 32+ C
44+ B+ 29+ C–
41+ B

27+

D
38+ B– 0-26 F
Exam #1 solutions
Practice Exam #1   Solutions
    
Approximate letter grades for Exam #2
Total points on exam was 36. Median score was 33
Mean score was 32.4. Standard deviation was 3.5.
score grade   score grade
34+ A 23+ C+
31+ A– 21+ C
29+ B+ 19+ C–
27+ B

17+

D
25+ B– 0-16 F
Exam #2 solutions
Practice Exam #2   Solutions
Approximate letter grades for Exam #3
Total points on exam was 36. Median score was 32.5.
Mean score was 30.2. Standard deviation was 4.8.
score grade   score grade
33+ A 23+ C+
31+ A– 21+ C
29+ B+ 19+ C–
27+ B

17+

D
25+ B– 0-16 F
Exam #3 solutions
Practice Questions for Exam #3    Solutions
 
Approximate letter grades for Exam #4
Total points on exam was 36. Median score was 31.5.
Mean score was 29.2. Standard deviation was 6.3.
score grade   score grade
33+ A 23+ C+
31+ A– 21+ C
29+ B+ 19+ C–
27+ B

16+

D
25+ B– 0-15 F
Exam #4 solutions
Practice Questions for Exam #4    Solutions

Concourse Mathematics Tutoring Schedule
Tutor Course Day, Time Notes
Camille Everhart primarily 18.01A Mondays, 5-7pm  
Kaiying Liao 18.01A and 18.02 Mondays, 8-10pm  
Colleen Loynachan 18.01A Tuesdays from 8-10pm Hours may change when PS due dates are changed
Marie Perrone 18.02 only Wednesdays, 5-7pm  
John Mikhael 18.01A and 18.02 Wednesdays, 6-8pm Hours may change to day before Psets are due.
Sebastián Vélez primarily 18.02 Wednesdays, 7-9  
Bobby Fortanely      

Topics and Assignments are posted in the Course Calendar.

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

Solutions to PS #1 through PS #5 are now posted on the Solutions page.


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.

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.

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)

Syllabus for Concourse Math 18.02     Printable syllabus (PDF)    B&W version (PDF)
These may still be revised slightly.


If ever the MIT mail servers are not accessible from the outside world and you need to get in touch, you can also 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 31, 2012 6:41 PM