Fall 2017
Multivariable Calculus
Math 18.02, Concourse - MIT
Fall 2017

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 Wed, Dec 20.

Approximate letter grades for Exam #1
Total points on exam was 50. Median score was 43.
Mean score was 41.2. Standard deviation was 6.4.
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
 
Approximate letter grades for Exam #2
Total points on exam was 50. Median score was 50.
Mean score was 48.2. Standard deviation was 2.4.
score grade   score grade
47+ A 34+ C+
45+ A– 31+ C
43+ B+ 28+ C–
40+ B 25+ D
37+ B– 0-24 F
Approximate letter grades for Exam #3
Total points on exam was 48. Median score was 48.
Mean score was 46.1. Standard deviation was 3.9.
score grade   score grade
46+ A 32+ C+
44+ A– 29+ C
41+ B+ 26+ C–
38+ B 24+ D
35+ B– 0-23 F
 
Approximate letter grades for Exam #4
Total points on exam was 50. Median score was 43.
Mean score was 42.4. Standard deviation was 8.4.
score grade   score grade
45+ A 31+ C+
43+ A– 29+ C
40+ B+ 27+ C–
37+ B 25+ D
34+ B– 0-24 F
Approximate letter grades for Final Exam
Total points on exam was 100. Median score was 88.
Mean score was 84. Standard deviation was 12.8.
score grade   score grade
92+ A 66+ C+
87+ A– 61+ C
82+ B+ 56+ C–
77+ B 50+ D
72+ B– 0-49 F

Exam #4 took place on Thurs, Dec7.


Problem Set #10 (due Wed, Dec 6)
References: 15.6 (The Divergence Theorem); Notes V10 (The Divergence Theorem); RW-Orthogonal Curvilinear Coordinates - Div, grad, curl, and Laplacian; 15.7 (Stokes' Theorem); Notes V13 (Stokes' Theorem); Notes V14 (Some Topological Questions); Notes V15 (Relations to Physics); and Lecture Notes.


Problem Set #9 (due Wed, Nov 29)
References: Notes V3 (Two-dimensional Flux); Notes V4 (Green's Theorem in Normal Form); 14.8 (Surface Area); Notes V7 (Laplace's Equation and Harmonic Functions); 15.5 (Surface Integrals); Notes V9 (Surface Integrals); RW-Supplement on surface integrals; 15.6 (The Divergence Theorem); Notes V10 (The Divergence Theorem); and Lecture Notes.


Exam #3 took place on Thursday, Nov 16.


Problem Set #8 (due Thurs, Nov 16)
References: 15.1 (Vector Fields, Divergence and Curl); Notes V1 (Plane Vector Fields); Notes V8 (Vector Fields in Space); 15.2 (Line Integrals); Notes V11 (Line Integrals in Space); 15.3 (Fundamental Theorem and Independence of Path); Notes V2 (Gradient Fields and Exact Differentials); Notes V12 (Gradient Fields in Space); 15.4 (Green's Theorem); and Lecture Notes.


Problem Set #7 (due Wed, 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.


Exam #2 took place on Tues, Oct 24. 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, the Method of Lagrange Multipliers, and derivatives involving non-independent variables.


Problem Set #6 (due Tues, Oct 31)
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)


Problem Set #5 (due Fri, Oct 20)
References: 13.5 (Multivariable Optimization Problems), 13.9 (Lagrange Multipliers and Constrained Optimization)


Exam #1 took place on Tues, Oct 3.
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 vectors, curvature; partial derivatives, linear approximation, gradient, 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 #4 (due Fri, Oct 13)
References: 13.7 (Chain Rule and Implicit Differentiation), 13.8 (Directional Derivatives and the Gradient); Supplement on the Chain Rule and Implicit Differentiation; Supplementary Notes TA (Tangent Approximation), 13.5 (Multivariable Optimization Problems), 13.10 (Critical Points of Functions of Two Variables and the Second Derivative Test); Supplementary Notes LS (Least Squares Interpolation), and Lecture Notes.


Problem Set #3 (due Mon, Oct 2)
References: Read section 12.7 (Quadric Surfaces); Read sections 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.


Problem Set #2 (due Mon, Sept 25)
References: Read sections 10.4 (Parametric Curves), 12.5 (Curves and Motions in Space), 12.6 (Curvature and Acceleration), and appropriate sections from the Supplementary Notes (1F, 1G, 1H, 1J); Supplement: Vector and matrix forms of a system of linear equations, matrix algebra, inverse matrices, and related facts (not essential, but helpful if you want more prespective on Linear Algebra); D. Determinants (4 pages); Exercises for Vectors and Matrices (1A to 1K, 12 pages); Parameterized Curves (3 pages)


Problem Set #1 (due Thurs, Sept 14)


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: Wednesday, December 27, 2017 10:09 AM