Math 223 - Multivariable Calculus
Fall 2026
Emily Proctor




Please read the syllabus to learn all the details about the course.




Homework

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Week beginning September 14

Due Wednesday, September 16:

• Please type (up to) a page about who you are as a mathematician (classes or experiences you've had, anything you've liked, anything you've disliked...) as well as your motivations for taking Multivariable Calculus this semester. Be honest; this is just a simple, informal assignment that will help me start to get to know you. If there is anything else you'd like me to know as we start the semester, please include that too. Print out two copies of your page and turn them in at the start of class on Wednesday.


• Order or obtain a copy of our textbook, Calculus, Early Transcendentals, 9th ed. by James Stewart, et al.


• Read Section 12.1.

Due Friday, September 18:

• From Section 12.1 do problems: 3, 4, 6, 10, 15, 17, 19*, 30, 31, 35, 39, 45.


• *For Problem 12.1.19, see Example 6, p.834.


• Read Section 12.2.

Week beginning Septebmer 21

Due Monday, September 21:

• From Section 12.2 do problems: 4, 7, 9, 16, 21, 25, 26, 45, 46, 47.


• Read Sections 12.3 and 12.4.

Due Wednesday, September 23:

• From Section 12.3 do problems: 1, 8, 11, 15, 24, 41, 64*.


• From Section 12.4 do problems: 3, 11, 13, 14, 17, 20, 29.


• *Hint for 12.3.64: start with a dot product.


• Read Sections 12.5.

Due Friday, September 25:

• From Section 12.5 do problems: 3, 4, 5, 9 (parametric only), 10 (parametric only), 17, 19, 24, 29, 31, 41, 45, 51, 64a.


• Read Section 12.6.

Week beginning September 28

Due Monday, Septebmer 28:

• From Section 12.6 do problems: 1, 6, 10, 23, 24, 25, 26, 27, 28, 29, 30, 31, 46, 47, 48.


• Read Section 13.1.

Due Wednesday, September 30:

• From Section 13.1 do problems: 7, 14, 21, 25, 26, 27, 28, 29, 30, 35, 39, 52, 53, 57.


• Read Sections 13.2, 13.3 (p.904-905), and 13.4 (p.916-917).

Due Friday, October 2:

• From Section 13.2 do problems: 10, 19, 25, 35.


• From Section 13.3 do problems: 1, 4.


• From Section 13.4 do problems: 3, 9, 15, 22*.


• *Hint for 13.4.22: see the proof of Theorem 13.2.4.


• Read Section 14.1.

Week beginning October 5

Due Monday, October 5:

• From Section 14.1 do problems: 3, 21, 28, 35, 36, 46, 61, 62, 63, 64, 65, 66, 67, 70.


• Read Section 14.2.

Due Wednesday, October 7:

• From Section 14.2 do problems: 5, 9, 13, 14, 20, 22*, 37, 43, 44, 51*.


• *Hint for 14.2.22: try factoring! For 14.2.51, try it out...I will pass out solutions!


• Read Section 14.3.

Due Friday, October 9:

• From Section 14.3 do problems: 3ab, 5, 6, 10, 14, 29, 37, 45, 55, 74, 95.


• Read Section 14.4.


• Our first midterm will be next Tuesday, October 13, 7-9pm, in Warner 105. On Monday, October 12, we will use class for an optional review session. Our exam will cover from the beginning of the year, through Section 14.4 of Stewart. Here is a list of topics to help as you review!


• In order to help you prepare for our exam next week, here is a practice exam in the style of our midterm. And here are the solutions.

Week beginning October 12

Due Monday, October 12:

• From Section 14.4 do problems: 1, 5, 19*, 25, 27.


• *Hint for 14.4.19: see Theorem 8 p.977.


• Here is the tangent plane/linearization example that we looked at in class on Friday.


• If you'd like to keep a copy of your homework, I will pass out solutions to this assignment on Monday after you've turned it in so that you can check your work.


• Prepare for our exam on Tuesday. Monday's class will be a review session. I won't come with an agenda so please bring any questions and we will talk about them!

Due Wednesday, October 14:

• Read Section 14.5.

Week beginning October 19

Due Monday, October 19:

• From Section 14.5 do problems: 1, 7, 11, 18, 19, 22, 25 (z_u only), 39, 40.


• Read Section 14.6.


• Please take a moment to fill out this short survey from the Q-center. Your response really helps!

Due Wednesday, October 21:

• From Section 14.6 do problems: 1, 5, 6, 13, 19, 23, 34*.


• *The computations for Problem 14.6.34 get a little messy. Once you have your strategy for solving the problem, stick with it and hang in there!


• Read Section 14.6, p.997-1001.

Due Friday, October 23:

• From Section 14.6 do problems: 9, 20, 26, 28, 33, 39, 41, 43ab.


• Read Section 14.6, p.1002-1004.

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Week beginning October 26

Due Monday, October 26:

• From Section 14.6 do problems: 49, 52, 55, 57, 62, 73, 74, 75*.


• *For Problem 14.6.75, assume f is differentiable.


• Read 14.7.

Due Wednesday, October 28:

• From Section 14.7 do problems: 3, 5, 10, 19, 45*.


• *For Problem 14.7.45, make an (intuitive) argument that you have found the points that give an absolute minimum for the distance. Also, note that minimizing the square of the distance gives the same result as minimizing the distance, but the math is a lot easier!


• Read Section 14.8.

Due Friday, October 30:

• From Section 14.8 do problems: 1, 6, 9*, 28**,43.


• *To solve the system in Problem 14.8.9, try getting x, y, and z in terms of lambda, then using the constraint.


• **For Problem 14.8.28, try using the Extreme Value Theorem here. Example 4 on p.1024 is a good model (see Example 7 on p.1015 for another example of the concept).


• Read Section 15.1.

Week beginning November 2

Due Monday, November 2:

• From Section 15.1 do problems: 1a, 7a, 9, 11, 15, 28, 37, 39a, 47, 48.


• Read Section 15.2.