Math 3298 Multivariable Calculus Syllabus, Fall 2017

This page will be updated throughout the semester.

Practice tests     Worksheets     Homework     Labs     Resources

Instructor:

Dr. Marshall Hampton

Office: 172 SCC

Email: mhampton at d.umn.edu (preferred contact method)

Telephone: 726-6329

Office hours: 12:00 - 1:30 Monday, Tuesday, and Wednesday.

Class homepage:
http://www.d.umn.edu/~mhampton/m3298f17.html (this page)

Lecture Times:
Section 001: 9:00 P.M. - 9:50 P.M., M, W, Th, F (8/28/2017 - 12/8/2017), SCC 21.

Lab (002) Times:
9:00 P.M. - 9:50 P.M., Tu, MonH 209

Lab TA: Zhenduo Wang.

Prerequisites:
Math 1297 (Calculus II) or equivalent.

Student Conduct Code:
see the full description at http://regents.umn.edu/sites/default/files/policies/Student_Conduct_Code.pdf.
Note that while collaborating on homework and lab assignments is encouraged, it is not acceptable to simply copy another person's work.

Textbook:
Calculus, Early Transcendental Functions, by James Stewart, is our primary textbook. It does not matter which edition of the text you have.

Topics:
This course will extend your knowledge of calculus to higher dimensions. We will cover chapters 12-16 from the text:


Exams:
There will be two midterms (10/6 (Exam A) and 11/10 (Exam B)) and a final exam (12/15, 8-10 am, exam F). A calculator and sheet of notes is allowed on each exam. For the final you can use two pages of notes.

Practice midterm 1

Practice midterm 1 solutions

Practice midterm 2

Practice midterm 2 solutions

Practice final

Practice final solutions

In the learning objectives below, W=worksheet, H=homework, L = labs, A=midterm 1, B=midterm 2, and F = final.
Learning Objectives Required by the Higher Learning Commission.
  1. Find equations for lines and planes from different input data.(H,W,A,F)
  2. Compute and interpret cross and dot products of vectors.(H,W,A,F)
  3. Recognize and classify quadric surfaces.(H,W,L,A,F)
  4. Compute the arclength and curvature of 2D and 3D curves.(H,W,A,F)
  5. Compute the unit tangent, normal, and binormal vectors for a curve.(H,W,A,F)
  6. Sketch and interpret contour maps of functions.(H,W,L,A,F)
  7. Compute and interpret partial derivatives.(H,W,A,F)
  8. Compute tangent planes and linearizations of multivariate functions.(H,W,A,F)
  9. Compute and interpret directional derivatives and the gradient.(H,W,A,F)
  10. Use the chain rule for compositions of multivariate functions.(H,W,A,F)
  11. Find maxima and minima of multivariate functions, constrained or unconstrained.(H,W,L,A,F)
  12. Compute double integrals both symbolically and numerically.(H,W,L,A,F)
  13. Compute multivariate integrals both symbolically and numerically.(H,W,L,B,F)
  14. Compute and interpret scalar and vector line integrals.(H,W,B,F)
  15. Compute and interpret the curl, divergence, and integrals of vector fields.(H,W,B,F)
  16. Use Green's theorem and Stokes' theorem to compute vector integrals.(H,W,B,F)

Calculator Policy:
Calculators are allowed during exams (note: an internet-capable device is not considered a calculator). However, you are expected to show the steps that justify your answers, and to give exact answers whenever possible. This also applies to homework unless the question specifically instructs you to use a computer or calculator. On a test, any step on which you use a calculator must be clearly indicated (just write "CALCULATOR" or "CALC").

Grading:
Grades will be based on your understanding of the material as demonstrated by class participation (mainly worksheets), office hours, homework, labs, and exams. The homework assignments will be weighted equally, with the lowest score dropped. The lowest lab score will also be dropped. The lowest three worksheet scores will be dropped. The approximate weighting is homework is 20%, each midterm 15%, labs 10%, worksheets 15%, and the final exam is 25%. Note that I do not use traditional grading percentages, although generally a score of around 90% of the total is sufficent for an A.


Worksheets:
W 1 Lines and planes in 3D.
W 2 Quadric surfaces.
W 3 Arclength.
W 4 Curvature, tangents, and normals.
W 5 Limits and continuity of multivariate functions.
W 6 Partial derivatives and linearization.
W 7 Directional derivatives.
W 8 Multivariate chain rule.
W 9 Unconstrained max/min.
W 10 Lagrange multipliers.
W 11 Closed set extrema.
W 12 Curve and surface review.
W 13 Iterated integrals.
W 14 Double integrals.
W 15 Polar integrals.
W 16 More polar integration.
W 17 Moments.
W 18 Curvature.
W 19 Multivariate extrema.
W 20 Review.
W 21 Spherical coordinates.
W 22 Triple integrals.
W 23 Spherical coordinate integrals.
W 24 Changing cooordinates.
W 25 Cylindrical and spherical integrals.
W 26 Xavier and Yolanda: a probabilistic tragedy..
W 27 Vector line integrals.
W 28 Potential functions.
W 29 Scalar line integrals.
W 30 Div, grad, curl.
W 31 Green's theorem.
W 32 Astroid area.
W 33 Surface integrals.
W 34 More surface area.
W 35 Multiple integral review.
W 36 Ungraded review.
W 37 Surface flux integral.
W 38 More surface flux integral practice.
W 39 Stokes' theorem.
W 40 Divergence theorem.
W 41 Integral theorem review.
W 42 Multivariate Newton's method.
W 43 Divergence theorem and Stokes' theorem practice.
W 44 Line integral review.
W 45 Constrained extrema problem.
W 46 Maxima and minima, directional derivatives.
W 47 Review (cross product, tangent plane, 3d integration).
W 48 Curvature of surfaces.

Homework:
Late homework is not accepted without a prior arrangement. Your answers should include intermediate steps - it is not acceptable to only write down an answer.

Assignment 1 (due Tuesday, September 5th).

Assignment 2 (due Wednesday, September 13th).

Assignment 3 (due Wednesday, September 20th).

Assignment 4 (due Wednesday, September 27th).

Assignment 5 (due Wednesday, October 4th).

Assignment 6 (due Friday, October 13th).

Assignment 7 (due Monday, October 30th).

Assignment 8 (due Tuesday November 7th).

Assignment 9 (due Wednesday November 15th).

Assignment 10 (due Wednesday November 22nd).

Assignment 11 (due Friday December 1st).

Labs:

We will use the computer algebra system Sage for our labs. Sage can be accessed through a browser at CoCalc or https://sage2.d.umn.edu:8008/

The two servers are not synchronized so if you wish to switch, you need to make accounts separately on each, and download/upload your lab. On the sage2 server, worksheets are stored as ".sws" files, while on CoCalc they are ".sagews" files. If you upload and open a sws file on CoCalc, it will automatically convert it to the sagews file type.

Lab 1 on sage2 server (due Thursday, September 21th).

Lab 2 on sage2 server (due Thursday, September 28th).

Lab 3 on sage2 server (due Thursday, October 5th).

Lab 4 on sage2 server (due Thursday, October 12th).

Lab 5 on sage2 server (due Thursday, November 2nd).

Lab 6 on sage2 server (due Thursday, November 16th).

Lab 7 on sage2 server (due Thursday, November 30th).

Optional lab on sage2 server (due Friday, December 8th, email the sws file to mhampton).

It may be helpful to read this introduction, written by professor Gregory Bard of UW Stout. There is also another interesting book on Sage which is currently under development.

Other resources:

Interactive introduction to Python. This might be easier to use than the CodeAcademy site.


Code Academy's brief intro to Python. A good interactive tutorial on the basics of the Python language.

Policy statement:
The University of Minnesota is committed to the policy that all persons shall have equal access to its programs, facilities, and employment without regard to race, religion, color, sex, national origin, handicap, age, veteran status, or sexual orientation.

Disabilities:
An individual who has a disability, either permanent or temporary, which might affect his/her ability to perform in this class should contact the instructor as soon as possible so that he can adapt methods, materials and/or tests as needed to provide for equitable participation.