Fall 2018
Multivariable Calculus
Math 18.02, Concourse - MIT
Fall 2018

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

Calendar of topics and
homework assignments
Solutions

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:

The Final Exam took place on Thursday, Dec 20 from 9:00am to noon in 16-160.
Approximate letter grades are shown below. Individual Final Exam grades are available on the Stellar site.
Note: Though the Final Exam scores varied widely, all students in the course quaified for a passing grade in the course.


Approximate letter grades for Exam #1
Total points on exam was 50. Median score was 44.
Mean score was 43.7. Standard deviation was 3.2.
score grade   score grade
45+ A 32+ C+
43+ A– 30+ C
41+ B+ 28+ C–
38+ B 26+ D
35+ B– 0-25 F
Practice Questions for Exam #1     Solutions
Exam #1 Solutions
     
Approximate letter grades for Exam #2
Total points on exam was 50. Median score was 48.
Mean score was 46.7. Standard deviation was 4.1.
score grade   score grade
46+ A 31+ C+
43+ A– 29+ C
40+ B+ 27+ C–
37+ B 25+ D
34+ B– 0-24 F
Practice Exam #2    Solutions
Exam #2 Solutions
Approximate letter grades for Exam #3
Total points on exam was 50. Median score was 47.
Mean score was 44.3. Standard deviation was 6.9.
score grade   score grade
46+ A 31+ C+
43+ A– 29+ C
40+ B+ 27+ C–
37+ B 25+ D
34+ B– 0-24 F
Exam #3 Practice Problems     Solutions
Exam #3 Solutions
 
Approximate letter grades for Exam #4
Total points on exam was 50. Median score was 34.
Mean score was 35.8. Standard deviation was 8.9.
score grade   score grade
45+ A 30+ C+
42+ A– 27+ C
39+ B+ 25+ C–
36+ B 23+ D
33+ B– 0-22 F
Practice Questions for Exam #4     Solutions
Exam #4 Solutions
Approximate letter grades for Final Exam
Total points on exam was 100. Median score was 82.
Mean score was 74.1. Standard deviation was 17.5.
score grade   score grade
90+ A 65+ C+
85+ A– 60+ C
80+ B+ 55+ C–
75+ B 50+ D
70+ B– 0-49 F

Problem Set #11 (due Fri, Dec 7)
References: See Course Calendar


Exam #4 took place on Thursday, Dec 6 during Recitation.
Exam Topics: 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, Stokes' Theorem.


Problem Set #10 (due Thurs, Nov 29)
References: See Course Calendar

Problem Set #9 (due Tues, Nov 20)
References: See Course Calendar


Exam #3 took place on Thurs, Nov 15 during Recitation. Topics included: Integration over two- and three-dimensional regions; double and triple integrals in Cartesian, cylindrical, and spherical coordinates; Fubini Theorem and interchanging order of integration; applications of integration – areas, volumes, mass, averaging, weighted averages, centroids and center of mass, moment of inertia, general change of variables for double and triple integrals, Jacobian determinants.


Exam #2 took place on Tuesday, October 23. The exam covered partial derivatives, linear approximation, differentials, gradient vector, normal vectors to curves and surfaces, directional derivative, the Chain Rule, implicit differentiation, stationary points, second derivative test, optimization, and the Method of Lagrange Multipliers.


Problem Set #8 (due Thurs, Nov 8)
References: 14.6 (Triple Integrals), 14.7 (Integration in Cylindrical and Spherical Coordinates), 14.8 (Surface Area), 14.9 (Change of Variables in Multiple Integrals); SN-I. Limits in Iterated Integrals; SN-CV. Changing Variables in Multiple Integrals; SN-G. Gravitational Attraction; and Lecture Notes.


Problem Set #7 (due Thurs, Nov 1)
References: SN-N. Non-independent Variables (8 pages); 14.1 (Double Integrals); 14.2 (Double Integrals Over More General Regions); 14.3 (Area and Volume by Double Integration); 14.4 (Double Integrals in Polar Coordinates); 14.5 (Applications of Double Integrals); SN-I. Limits in Iterated Integrals (4 pages); and Lecture Notes.


Problem Set #6 (due Thurs, Oct 18) - You may use any method unless a particular method is specified.
References: Read sections 13.5 (Multivariable Optimization Problems), 13.9 (Lagrange Multipliers and Constrained Optimization).


The first Midterm Exam took place on Tues, Oct 2.
Exam topics: Vectors and vector algebra, dot product, cross product, applications to working with lines and planes, areas, volumes, angles, etc.; parameterized curves, velocity vectors, speed, arclength, unit tangent and normal vectors; partial derivatives, linear approximation, differentials, and directional derivative. You should also be familiar with methods for solving systems of linear equations (such as when finding the intersection of lines or planes) and related matrix ideas.


Problem Set #5 (due Fri, Oct 12)
References: Read sections 13.7 (Chain Rule and Implicit Differentiation), 13.8 (Directional Derivatives and the Gradient); the Supplement on the Chain Rule and Implicit Differentiation; and Supplementary Notes TA (Tangent Approximation), 13.10 (Critical Points of Functions of Two Variables and the Second Derivative Test); and Supplementary Notes LS (Least Squares Interpolation).

Problem Set #4 (due Fri, Oct 5)
References: Read sections 12.7 (Quadric Surfaces); 13.1-13.2 (Functions of Several Variables); 13.3 (Limits and Continuity);
13.4 (Partial Derivatives); 13.6 (Increments and Linear Approximation); Supplementary Notes TA (Tangent Approximation); and Lecture Notes.


Syllabus for Concourse Math 18.02     Printable syllabus (PDF)

Topics and Assignments are posted in the Course Calendar.

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)


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: Saturday, December 22, 2018 1:15 AM