Welcome to the permanent home page for Section WBP01 of MATH-2080 (Calculus 3) at Southeast Community College in the Fall term of 2021. I am Toby Bartels, the instructor.

Course administration

Contact information

I am often available outside of those times; feel free to send a message any time.


The official textbook for the course is the 4th Edition of University Calculus: Early Transcendentals by Hass et al published by Addison Wesley (Pearson). You will automatically get an online version of this textbook through Canvas, although you can use a print version instead if you like. This comes with access to Pearson MyLabs, integrated into Canvas, on which many of the assignments appear. There is also a packet of course notes (DjVu).

Curves and functions

  1. General review:
  2. Parametrized curves:
  3. Standard parametrizations:
  4. Integrating parametrized curves:
  5. Arclength:
  6. Functions of several variables:
  7. Topology in several variables:
  8. Limits in several variables:
  9. Vector fields:
  10. Linear differential forms:
  11. Differentials:
Quiz 1, covering the material in Problem Sets 1–11, is available on September 17 Friday.


  1. Partial derivatives:
  2. Levels of differentiability:
  3. Directional derivatives:
  4. Gradient vector fields:
  5. Matrices:
  6. The Chain Rule:
  7. Tangent flats and normal lines:
  8. Linearization:
  9. Estimation:
  10. Local optimization:
  11. Constrained optimization:
  12. Lagrange multipliers:
Quiz 2, covering the material in Problem Sets 12–23, is available on March 4 Thursday.


  1. Integration on curves:
  2. Integrating vector fields:
  3. Integrating scalar fields:
  4. Double integrals on rectangles:
  5. Double integrals:
  6. Systems of inequalities:
  7. Triple integrals:
  8. Areas, volumes, and averages:
  9. The area element:
  10. Coordinate transformations:
  11. Polar coordinates:
  12. Area integrals in polar coordinates:
  13. Volume integrals in polar coordinates:
Quiz 3, covering the material in Problem Sets 24–36, is available on April 1 Thursday.

More integration

  1. Parametrized surfaces:
  2. Integrals along surfaces:
  3. Flux across surfaces:
  4. Integrals on surfaces:
  5. Moments:
  6. Conservative vector fields and exact differential forms:
  7. Exterior differentials:
  8. Green's Theorem:
  9. Stokes's Theorem:
  10. Gauss's Theorem:
  11. Cohomology:
Quiz 4, covering the material in Problem Sets 37–47, is available on April 22 Thursday.


  1. Curves and functions:
  2. Differentiation:
  3. Integration:
  4. More integration:

Final exam

There is a comprehensive final exam at the end of the term. (You'll arrange to take it some time from April 30 to May 6.) To speed up grading at the end of the term, the exam will be multiple choice, with no partial credit.

For the exam, you may use one sheet of notes that you wrote yourself; please take a scan or a picture of this (both sides) and submit it on Canvas. However, you may not use your book or anything else not written by you. You certainly should not talk to other people! Calculators are allowed, although you shouldn't really need one, but not communication devices (like cell phones).

The exam consists of questions similar in style and content to those in the practice final exam on MyLab.

The final exam will be proctored. In the face-to-face class, you can take it on May 4 Tuesday, in our normal classroom at the normal time but lasting until 2:40 PM. If you have access to a computer with a webcam, then you can schedule a time with me to take the exam in a Zoom meeting. If you're near Lincoln, then we can schedule a time for you to take the exam in person. If none of these will work for you, then contact me as soon as possible to make alternate arrangements.

This web page and the files linked from it were written by Toby Bartels, last edited on 2021 August 31. Toby reserves no legal rights to them.

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