Welcome to the permanent home page for Section WBP01 of MATH-2080 (Calculus 3) at Southeast Community College in the Spring term of 2023. I am Toby Bartels, your instructor.

Course administration

Contact information

Feel free to send a message at any time, even nights and weekends (although I'll be slower to respond then).


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 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 MyLab, 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. Matrices:
  7. Functions of several variables:
  8. Topology in several variables:
  9. Limits in several variables:
  10. Vector fields:
  11. Linear differential forms:
Quiz 1, covering the material in Problem Sets 1–11, is available on February 3 Friday and due on February 6 Monday.


  1. Differentials:
  2. Partial derivatives:
  3. Levels of differentiability:
  4. Directional derivatives:
  5. Gradient vector fields:
  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 3 Friday and due on March 6 Monday.


  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 March 31 Friday and due on April 3 Monday.

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 21 Friday and due on April 24 Monday.


  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 May 1–5.) To speed up grading at the end of the term, the exam is 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 exam on MyLab.

The final exam will be proctored. 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 you're near any of the three main SCC campuses (Lincoln, Beatrice, Milford) and available on a weekday, then you can schedule the exam at one of the Testing Centers. 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 (except for the official syllabus) were written by Toby Bartels, last edited on 2023 March 5. Toby reserves no legal rights to them.

The permanent URI of this web page is