Spring 2019

Emily Proctor

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

- Week beginning: February 11
- Due Wednesday, February 13:
- Read Sections 1.1-1.4. (Note: you won't be responsible for knowing about the symmetric form of a line in R^n.)
- From Section 1.1 do problems: 6, 7, 10, 15, 17, 19 (property 2 only), 21a, 22, 23.
- From Section 1.2 do problems: 9, 10, 11, 17, 19, 28, 30, 35, 43.
- Here the notes that I presented in class today, as well as an expanded version of the same notes. Both would be worth a look, to help you review and orient yourself towards some of the ways we will be thinking about vectors in this class. They are related to the material in Sections 1.1 and 1.2 of our book.
- In case you would like to look at them in advance, here are the notes that I will be using in Wednesday's class.

- Week beginning February 18
- Due Monday, February 18:
- Read Section 1.5. As part of class on Monday, I'm going to talk a bit about the parametric equations of a plane. With this in mind, it might help you to go back before class and take a look again at Problem 1.1.22.
- From Section 1.3 do problems: 3, 9, 15, 18, 20, 21, 22 (property 3 only), 25, 33.
- From Section 1.4 do problems: 5 (it's okay to compute just one way), 9, 13, 17, 23, 25, 26.
- Here again are the notes from Wednesday's class.
- If you would like to look at them in advance, here are the notes that I will be using for class on Monday. We probably won't get into the material that comes from Section 1.6 (Cauchy-Schwarz and Triangle Inequality), but I think it can't hurt to see it now in any case.

- Due Wednesday, February 20:
- Read Section 1.6 (p.48-51) and Section 1.7
- From Section 1.5 do problems: 1, 4, 8, 11, 12, 14, 16, 19, 22, 23, 25. (Problem 25 is a distance problem. Even though we didn't cover the method in class, I put this problem on the assignment to prompt you to read Examples 7, 8, and 9 in the book. The goal is to help you understand material about projections and dot products better, so reading these examples is as important as doing the problem.)

- Due Friday, February 22:
- Read Section 2.1.
- From Section 1.6 do problems: 6, 9, 10, 11, 12.
- From Section 1.7 do problems: 1, 9, 11, 15, 18, 19, 20a, 23, 26, 29, 32, 33, 35 (see hint below), 38, 42ab (see note below).
- Here is another example using cylindrical coordinates that I hope might be of use as you prepare to do your homework.
- Hint for 1.7.35: There are two inequalities given in Problem 35: 2cos(phi)\leq rho and rho\leq 3. Consider each separately. For the first, try multiplying through by rho.
- For 1.7.42, make note of which method for describing the given region is simpler. Later on, when we are integrating in three dimensions, this type of thinking will help you to set up integrals so that they are as simple to compute as possible.
- If you are interested in looking at the proofs of the Cauchy-Schwarz and Triangle Inequalities, here are the notes one more time!

- Week beginning Monday, February 25
- Due Monday, February 25:
- Reread Section 2.1, paying extra attention to p.92-95. We started talking in class about how graphs of functions from R^2 to R are examples of surfaces in R^3. The material on p.92-95 talks more generally about how surfaces arise in R^3.
- There are no problems due on Monday. (I hope you enjoy a little sun on Saturday!)
- I have posted the problems due on Wednesday already in case you'd like to get started. You have the background at this point to do 2.1: 2abc, 5, 11, 13. Class on Monday will probably be more meaningful for you if you try 15 and 17 ahead of time too.

- Due Wednesday, February 27:
- Read Section 2.2. This is a relatively long section, but the author does a good job of describing things, so take the time to read it carefully. You do not need to read the addendum at the end unless you are curious.
- From Section 2.1, do problems: 2abc, 5, 11, 13, 15, 17, 22, 29, 32*, 33, 37, 38**, 39, 40, 41, 42, 46.
- *Problems 2.1.32, 33, and 37 are just asking for some level surfaces. You do not need to put them together into a graph (it would be impossible!).
- **Problem 2.1.38 is highlighting an important concept. Pay attention to this one, in conjunction with your class notes from today and the italicized comment in the middle of p.93.
- If you looking to practice some more with cylindrical and spherical coordinates, problems 1.7.23-35 would be good extra problems to play with. These are completely optional, to work on on your own, as much or as little as you like.

- Due Friday, March 1:
- Read Section 2.3, p.116-118 and Section 2.4, p.136-138.
- From Section 2.2, do problems: 3, 7, 8, 11, 12, 13, 19, 23, 33, 35, 39*, 45*. 47.
- *Briefly justify your answers for problems 2.2.39 and 45.

- Week beginning Monday, March 4
- Due Monday, March 4:
- Read Section 2.3, p.118-123
- From Section 2.3 do problems: 2, 3, 5, 8, 13, 14.
- From Section 2.4 do problems: 11, 14, 16, 22abcd, 23, 28.

- Due Wednesday, March 6:
- Read Section 2.3, p.123-128. Read Section 2.4, p.133-135.
- From Section 2.3, do problems: 35, 37, 40, 42, 45.
- In case it is helpful, here is an example of how to compute the equation for a tangent plane.
- The reading for tonight describes an important concept. Since there are fewer problems due than usual, spend some extra time reading carefully. To this end, problem 45 is a bridge between what we covered in class on Monday and what you are reading about for Wednesday.
- Keep preparing for our exam on Monday of next week.

- Due Friday, March 8:
- Read Section 2.5.
- From Section 2.3 do problems: 26, 27, 33, 44, 59.
- From Section 2.4 do problems: 2, 5.
- We didn't get to these in class, but Theorems 3.9, 3.10, and 3.11 on p.127 are handy. Theorem 3.10 in particular is the multidimensional version of one we've already talked about.
- As I mentioned in class, the material from the end of class about the interpretation of the derivative goes into a bit more depth than the book does. Since we'll be thinking this way later on in the semester, it would be worth it to take another look or two at your notes now to help that material sink in.

- Week beginning March 11:
- Due Monday, March 11:
- Continue to prepare for the exam on Monday night. The exam will cover up through Sections 2.3 and 2.4 and will take place in Warner 208.
- Monday's class will be an optional review session. I won't come with an agenda, so please bring any questions you have!

- Due Wednesday, March 13:
- Read Section 2.6 p.158-163.
- From Section 2.5 do problems: 2, 3, 4, 5, 8, 11, 13, 24, 25, 28, 29.

- Due Friday, March 15:
- Read Section 3.1, p.189-193.
- From Section 2.6 do problems: 1, 2, 3, 6, 9ab, 11, 12, 13.

- Week beginning March 18
- Due Monday, March 18:
- Read Section 2.6 p. 164-168.
- From Section 3.1 do problems: 3, 5, 9, 11b*, 12b*, 17 (give a vector equation), 19, 25**, 27, 29***, 30, 33.
- * For Problems 11b and 12b, you do not need the pictures from parts a in order to do parts b.
- ** If you would like it, here is a description about how to think about Problem 25.
- *** In Problem 29, note that if ||x(t)|| is constant, then so is ||x(t)||^2. Problem 27 might be of help here.
- In order to make Monday's class more meaningful, if it's not quite feeling comfortable to you yet, it's a good time to review the notion that every surface in R^3 can be thought of as the level surface of some function.