In Fall 2024 I taught multivariable calculus at MIT for my TA duties. This page lists materials I wrote in this process.

The LAMV textbook

• Download the most recent draft (updated PDF).
  • There’s also a Stokes theorem poster.
• All the source code is on GitHub, in vEnhance/1802.
• If you spot an issue or have proposed edits, please either
  • Raise an issue in GitHub, or
  • Open a pull request if you know how that works.
• Comments, suggestions, words of encouragement, notes of gratitude, pictures of bunnies, etc., are welcome at my usual email.
• More generally, see CONTRIBUTING.md for ways you can help out, ranging from finding typos (there are plenty) to writing new content and anything in between.
• As indicated in the GitHub, these notes are under MIT License. For example, if you’re an instructor teaching a multivariable calculus class, you are welcome to use these notes for your course however is helpful to you with attribution; you don’t need additional written permission from me.
• See also Poonen’s fall 2021 notes.

Historical recitation handouts

My recitation sections in Fall 2024 met on Monday and Wednesdays at 9am. The handouts for these recitations are archived here for historical reasons, but the book above is likely to be more useful to you. Most recitation handouts consist of

• A copy-pasted excerpt of from the textbook above, abridged to fit on one sheet of paper
• Some practice questions provided by the instructor for the course
• An answer key generated by ChatGPT (not edited/checked/polished at all, so use at your own peril)

Source code for these files are posted on GitHub.

• R01 09/04 Welcome and type safety
  • Programmers in the room might enjoy this 4-minute talk
• R02 09/09 Normal vec, dot and cross prod and answer key
  • Appendix: proof of dot product property
• R03 09/11 Encoding lin maps as matrices and answer key
• R04 09/16 Lin indp, span, basis and answer key
• R05 09/18 Eigenthings and answer key
• R06 09/23 Complex nums and answer key
• R07 09/25 Review for midterm 1 and answer key
• R08 09/29 Parametric and answer key
• R09 10/02 Parametric cont’d, gradients and answer key
• R10 10/07 Gradients and answer key
• R11 10/09 Min-max and answer key
• R12 10/16 Min-max and LM and answer key
• No special notes for October 21; review for midterm 2
  • Mock midterm 2 on Monday, October 21, 2024, from 3pm-4pm
• R13 10/23 Double integral and answer key
• R14 10/28 Double int, polar coord and answer key
• R15 10/30 Change var and answer key
• R16 11/04 Work and answer key
• R17 11/06 Anti-grad and answer key
• No special notes for November 13, review for midterm 3
  • Mock midterm 3 on Wednesday, November 13, 2024, from 6pm-8pm
• R18 11/18 Triple integral and answer key
• R19 11/20 Spherical and answer key
• R20 11/25 Surface and flux and answer key
  • Evan was out of town this day, so this is just the actual worksheet
• R21 12/02 Surf int and answer key
• R22 12/04 Div thm and answer key
• R23 12/09 Curl and crummy Stokes andanswer key
• R24 12/11 Goodbye