Multivariable Calculus

Professor: Erika L.C. King

Email: eking@hws.edu

Office: Lansing 304

Phone: (315) 781-3355

Home Page

Office Hours: MW 1-2PM; T 3:15-4:30PM, R 11AM-Noon; and by appointment

Class Schedule: held MWF 10:10AM-11:05AM in Napier 201

Course Syllabus

Course Grade Scale

**Review Session: Thursday, May 4th 1:00PM-2:00PM in Napier 201**

**Office Hours:**

- Wednesday, May 3th 2:30PM-4:30PM
- Thursday, May 4th 10:00AM-NOON
- Friday, May 5th 2:00PM-4:00PM
- Monday, May 8th 11:00AM-NOON
- By appointment

**Final Exam: Monday, May 8th 1:30PM-4:30PM in Napier 201. Bring your journal!**

**Collected Homework (Due Monday, May 1, 10:10AM):**

- Remember that this is to be your own work.
- Complete Problems 22 and 32 from Section 15.4 (explain your work) (pages 1008-9).
- Complete Problems 8 and 12 (Hint: complete the square) from Section 15.6 (page 1022).
- Complete Problem 8 from Section 16.2 (page 1071).
- Be sure to justify your answers. Please staple your work and use pencil.

**Prepare the following Journal Homework for class Monday, May 1:**

- Read Section 16.2 pages 1062-1071.
- Work/write up problems 5, 7, 11, 13 and 15 (these last three involve curves in three-space, but they work much the same way, look carefully at what you are integrating with respect to) from Section 16.2 of the text (pg. 1071-1072).
- Optional problem: 3 on page 1071 (Section 16.2).

**There will be two speakers this week. Our very own Derrick Moore '05 will speak on Tuesday at 7:30PM in
Lansing 300. See the department website for more details. In addition, there
will be a candidate speaker on Thursday. Note that I will not be able to attend the Thursday talk. If you attend,
sign in with Prof. Orr so that you get credit for being there.**

**Our last collected assignment will be due the last day of class, Monday, May 1. **

**Prepare the following Journal Homework for class Wednesday, April 26:**

- Read Section 15.4 pages 1003-1007.
- Work/write up problems 7, 11, 15, 19, 25, 31 and 33 on pages 1008-9 (Section 15.4).
- Optional problems: 3, 5 and 29 on page 1008 (Section 15.4).

**Prepare the following Journal Homework for class Friday, April 28:**

- Read Section 15.6 pages 1019-1021.
- Work/write up problems 1, 5, 7, 21 and 23 on page 1022 (Section 15.6).
- Optional problems: 3, 9 and 11 on page 1022 (Section 15.6).

**Reminder: Our third exam is in class Friday, April 21st. Your journals will be collected
that day as well. Catch up on any journal problems left undone to help review for the exam (and
improve your journal grade!). There will be no additional collected assignment this week.**

**Prepare the following Journal Homework for class Monday, April 17:**

- Read Section 15.2 pages 989-94.
- Work/write up problems 9, 15, 17, 21 and 29 on pages 994-5 (Section 15.2).

**Prepare the following Journal Homework for class Wednesday, April 19:**

- Read Section 15.3 pages 995-1001.
- Work/write up problems 11, 15, 17, 25, 41 and 47 on pages 1002-3 (Section 15.3).
- Go over review sheet and prepare questions for class. Make a list of your top three questions.

**There will be two mathematics talks this week. One on Tuesday at 4:30 by John Carter and one on
Thursday at 4:00 by Angela Desai (CANCELED). Both talks will be in Lansing 300 and both will have refreshments beginning a half
hour before in Lansing 310.**

**Due to the talk on Tuesday, my office hours that day will be shortened to 3:15-3:45. There will be
opportunities for a few quick questions before and after the talk.**

**Prepare the following Journal Homework for class Monday, April 10:**

- Finish reading section 14.7 pages 959-61.
- Work/write up problems 29, 39, 41 and 43 on page 962 (Section 14.7).
- Optional problems: 33 and 37 (note that we could do this before - now try it with techniques from 14.7) on page 962 (Section 14.7).

**Prepare the following Journal Homework for class Wednesday, April 12:**

- Read section 14.8 pages 965-70.
- Work/write up problems 1, 5, 11, 19 and 39 (this one has two constraints!) on page 970-1 (Section 14.8).
- Optional problems: 29 and 31 (these are looking at exercises we did in 14.7 in a different way!) on page 971 (Section 14.8).

**Collected Homework (Due Friday, April 14, 10:10AM):**

- Remember that this is to be your own work.
- Complete this worksheet. (Full assignment available.)
- Be sure to justify your answers. Please staple your work and use pencil.

**Prepare the following Journal Homework for class Friday, April 14:**

- Finish the worksheet from class. You do not need to put this in your journal. We will spend ten minutes in groups on Friday before discussing the groupwork, but this should be more to check with your group that you all agree than for doing the problems from scratch. Groups will be presenting the problems. It would make sense to start class sitting with your group from Wednesday.
- Read Section 15.1 (pages 981-988).
- Work/write up problems 5, 7 and 13 on pages 988-9 (Section 15.1).
- Optional problem: 3 on page 988 (Section 15.1).

**Prepare the following Journal Homework for class Monday, April 3:**

- Read pages 940-7 of Section 14.6, paying special attention to the proof of Theorem 3 on pages 942-3.
- Work/write up problems 5, 9, 17, 25 and 29 on pages 950-1 (Section 14.6).
- Optional problems: 3, 7, 15, 19, 23 and 27 on pages 950-1 (Section 14.6).

**Prepare the following Journal Homework for class Wednesday, April 5:**

- Finish reading Section 14.6.
- Work/write up problems 31, 35 and 43 on pages 951-2 (Section 14.6).
- Optional problems: 33 and 41 on pages 951-2 (Section 14.6).
- Optional problems: These relate to the homework you got back on Monday. (1) There were two ways to do problem 4: implicit differentiation and our shortcut as a result of our chain rule work. You should knot both ways. In your journal, work the problem in the way you did not do it on your homework. (2) Repeat problem 3 showing that f_{xzy}=f_{yzx}=f_{zxy}. Note: the answer key to this assignment is (as usual) posted outside my office door.

**Collected Homework (Due Friday, April 7, 10:10AM):**

- Remember that this is to be your own work.
- Complete this worksheet. (Full assignment available.)
- Be sure to justify your answers. Please staple your work and use pencil.

**Prepare the following Journal Homework for class Friday, April 7:**

- Start reading Section 14.7 (pages 953-958).
- Work/write up problems 1, 3, 11, 13 and 17 on page 961 (Section 14.7).
- Optional problem: 15 on page 961 (Section 14.7).

**Prepare the following Journal Homework for class Monday, March 27:**

- Finish reading Section 14.4 in the text (pages 925-929).
- Work/write up problems 13, 15, 23 (make sure you have read about differentials on pages 927-929 first), 39 and 41 on pages 930-31 (Section 14.4).

**Prepare the following Journal Homework for class Wednesday, March 29:**

- Read Section 14.5 in the text (pages 931-937).
- Work/write up problems 9, 15, 23, 33, 39 and 43 on pages 938-9 (Section 14.5).
- Optional problems: 13, 19, 27, 35 and 45 on pages 938-9 (Section 14.5).

**Collected Homework (Due Friday, March 31, 10:10AM):**

- Remember that this is to be your own work.
- Complete this worksheet. (Full assignment available.)
- Be sure to justify your answers. Please staple your work and use pencil.

**Prepare the following Journal Homework for class Friday, March 31:**

- Finish the worksheet from class. (You need not put this in your journal.)
- Start reading Section 14.6 in the text.
- Work/write up problems 47 on page 939 (Section 14.5) and 1 on page 950 (Section 14.6).
- Catch up on journal work!

**Prepare the following Journal Homework for class Wednesday, March 22:**

- Rework in your journal any questions from the exam that are not due on Friday and for which you missed significant points.
- Read Section 14.3 in the text (pages 909-919).
- Work/write up problems 3 (see page 910), 5 (explain your answers), 9, 31, 43, 55 and 73 on pages 919-22 (Section 14.3).
- Optional problems: 21, 33, 37, 39, 45, 49, 59 and 69 on pages 920-1 (Section 14.3).

**Collected Homework/BONUS (Due Friday, March 24, 10:10AM):**

- Remember that this is to be your own work.
- Turn in your exam 2 with your assignment.
- Complete this worksheet. (Full assignment available.)
- Be sure to justify your answers. Please staple your work and use pencil.

**Prepare the following Journal Homework for class Friday, March 24:**

- Start reading Section 14.4 in the text (pages 923-925).
- Work/write up problem 85 on page 922 (Section 14.3).
- Work/write up problems 3, 5, 17 and 21 on page 930 (Section 14.4).

**There will be two computer science talks this week. One on Monday at 4:00 by Dr. Barbara Lerner and one on
Thursday by Marc Corliss.**

**Reminder: Our second exam is in class Wednesday, March 8th. Your journals will be collected
that day as well. Catch up on any journal problems left undone to help review for the exam (and
improve your journal grade!). There will be no additional collected assignment this week.**

**Prepare the following Journal Homework for class Monday, March 6:**

- Write the proof part of our last example from class on Friday. This does not need to go in your journal.
- Finish reading Section 14.2 in the text (pages 905-908).
- Work/write up problems 1, 11, 15, 23 and 33 on pages 908-9 (Section 14.2).
- Work/write up problems 17, 29 and 31 on pages 908-909 (Section 14.2).

**Thursday at 4:45PM in Lansing 300, Kristin Camenga, a graduate student in mathematics at Cornell University
will be speaking on "A Tale of Two Proofs".**

**Friday at 4:00PM in Lansing 300, Dr. Imre Tuba will be speaking on "Braids, Knots and Windows".**

**Prepare the following Journal Homework for class Monday, February 27:**

- Finish reading Section 13.4 in the text.
- Work/write up problems 41 and 45 on pages 869-70 (Section 13.3).
- Work/write up problems 5, 7, 13 and 15 on pages 878-79 (Section 13.4).

**Prepare the following Journal Homework for class Wednesday, March 1:**

- Finish reading Section 14.1 in the text (pages 887-897). There are some great pictures there.
- Work/write up problems 17(a) and 35 on page 879 (Section 13.4).
- Work/write up problems 5, 13, 30, 43 and 53-57 odd on pages 898-901 (Section 14.1).
- Optional problems: 35 page 879 (Section 13.4); 9, 15, 17, 35 pages 898-899 (Section 14.1).

**Prepare the following Journal Homework for class Friday, March 3:**

- Start reading Section 14.2 in the text (pgs. 902-904).
- Work problems 7, 9, 13, and 19 from Section 14.2 of the text (pg. 908).

**Collected Homework (Due Friday, March 3, 10:10AM):**

- Complete this worksheet. (Full assignment available.)
- Be sure to justify your answers. Please staple your work and use pencil.

**Prepare the following Journal Homework for class Monday, February 20:**

- Finish reading Section 13.2 in the text (pages 856-860).
- Work/write up problems 25, 29, 31, 35 and 39 on pages 861-2 (Section 13.2).
- Optional problems: 23 and 37 pages 862-3 (Section 13.2).

**Prepare the following Journal Homework for class Wednesday, February 22:**

- Start reading Section 13.3 in the text (pages 862-864).
- Work/write up problems 3, 9 and 11 on page 868 (Section 13.3).
- Optional problems: 1 and 5 page 868 (Section 13.3).

**Collected Homework (Due Friday, February 24, 10:10AM):**

- Complete this worksheet. (Full assignment available.)
- Be sure to justify your answers. Please staple your work and use pencil.

**Prepare the following Journal Homework for class Friday, February 24:**

- Finish reading Section 13.3 in the text (pages 864-868).
- Work/write up problems 15, 27, 33 and 39 on page 869 (Section 13.3).
- Optional problems: 19, 21 and 23 page 869 (Section 13.3).

**Note: We will have two computer science candidates speaking this week. Stephen Davies will speak on
Tuesday at 4PM and Paul Schermerhorn will speak on Wednesday at 4PM. Both talks will be in Lansing 300 with
refreshments being served beginning at 3:30 in Lansing 310. Remember that you are required to attend two talks
this semester, one of which should be mathematics and one which can be either mathematics or computer science.
You also can receive bonus points for attending additional talks.**

**Note: Because of the visiting candidates this week, my office hours on Tuesday and Wednesday will be
a little different. On Tuesday, I will be available to answer quick questions between 3:30 and 4:00. On
Wednesday my office hours will be 12:30-1:30. As always, if you need to see me and these times don't work
for you, please speak with me or email me to make an appointment.**

**Prepare the following Journal Homework for class Monday, February 13:**

- Read Section 12.6 in the text (pages 832-837).
- Work/write up problems 1, 11, 21-27 odd and 31 on pages 837-838 (Section 12.6).
- Optional problem: 7 page 837 (Section 12.6).

**Prepare the following Journal Homework for class Wednesday, February 15:**

- Read Section 13.1 in the text (pages 849-854).
- Work/write up problems 1, 3 (remember L'Hopital's Rule!), 13, 19-23 odd and 39 on pages 855-6 (Section 13.1).
- Optional problems: 7, 11, 15 and 25 page 855 (Section 13.1).

**Collected Homework (Due Friday, February 17, 10:10AM):**

- Remember that your only resources for these assignments are your notes, our textbook, me and your brain! Who could ask for more?!
- Complete this worksheet. (Full assignment shown.)
- Be sure to justify your answers. Please staple your work (if more than one page) and use pencil.

**Prepare the following Journal Homework for class Friday, February 17:**

- Start reading Section 13.2 in the text (pages 856-859).
- Work/write up problems 1, 7, 13, 15 and 19 on page 861 (Section 13.2).
- Optional problems: 3, 5 and 11 page 861 (Section 13.2).

**Reminder: Our first exam is in class Friday, February 10th. Your journals will be collected
that day as well. Catch up on any journal problems left undone to help review for the exam (and
improve your journal grade!). There will be no additional collected assignment this week.**

**Prepare the following Journal Homework for class Monday, February 6:**

- Read about planes in Section 12.5 in the text (pages 825-829).
- Work on the groupwork sheet from class on Friday. We will spend some time doing this Monday so be sure to bring it with you to class.
- Work/write up problems 1, 35, 37, 45 and 51 on pages 829-831 (Section 12.5).
- Optional problems: 5, 29, and 33 pages 829-830 (Section 12.5).

**Prepare the following Journal Homework for class Wednesday, February 8:**

- Finish any parts of the 12.5 groupwork sheets you have not completed. (These do NOT need to be in your journal.)
- Work/write up problems 55, 59, 63, 67 and 71 on page 831 (Section 12.5).
- Optional problem: 65 page 831 (Section 12.5).
- Catch up on your journal problems. I believe there are 48 of them. Make sure you did the right ones. (Always check that the section number and page number matches...if not, check with me. Thank you to those that caught my paginal error from last week. It is corrected now.) Make sure that it is easy for me to find each problem (section and number is the best way). Someone said they were planning on highlighting each problem number - a great idea! Today is the last day of problems for the journal.
- Look over the review sheet you received at the end of class. Be sure to bring it with you along with any questions you have to class on Wednesday.

**Remember that our first exam is a week from Friday! Make sure you are up to date with your journal work!**

**Prepare the following Journal Homework for class Monday, January
30:**

- Start reading Section 12.4 in the text (pages 814-816). Pay special attention to the proof of Theorem 6.
- Work/write up problems 7, 9, 11, 23 and 25 on page 820 (Section 12.4).
- Optional problems: 3, 13, 14, 17 page 820 (Section 12.4).

**Prepare the following Journal Homework for class Wednesday, February 1:**

- Finish reading Section 12.4 in the text (pages 817-820).
- Work/write up problems 33, 35, 37, 39 and 41 (without using components, just properties) on page 821 (Section 12.4).
- Optional problems: 29 and 31 page 821 (Section 12.4).

**Collected Homework (Due Friday, February 3, 10:10AM):**

- Complete this worksheet. (Now complete.)
- Be sure to justify your answers. Please staple your work (if more than one page) and use pencil.
- Remember that your only resources for these assignments are your notes, our textbook, me and your brain! More than sufficient for your needs!

**Prepare the following Journal Homework for class Friday, February 3:**

- Read about lines in Section 12.5 in the text (pages 822-825).
- Finish any parts of the groupwork sheet you did not complete in class on Wednesday.
- Work/write up problems 11, 15, 17 (see bottom of page 824 through the top of page 825), 21 and 41 on page 830 (Section 12.5).
- Optional problems: 3, 7 and 13 pages 829-830 (Section 12.5).

**Our first speaker is this Thursday at 3:30 in Lansing 300. See the department website for more details.**

**Note that some of my office hours this week will be used for individual meetings. Here are the group office
hours for this week only: M: 1-1:30, T: 3:15-3:50, W: 1-1:30 and R: 11:20-Noon. Please make an appointment if you
cannot make those times and need to see me. We will return to the normal schedule in week 3.**

**Prepare the following Journal Homework for class Monday, January
23:**

- Read Section 12.2 in the text (pages 798-804).
- Work/write up problems 11, 25, 27, 31 and 35 on pages 805-6 (Section 12.2). Remember to follow the guidelines in the syllabus.
- Optional problems (i.e. you should know how to do these, but don't need to put them in your journal): 3, 5, 15, 21 page 805 (Section 12.2). Doing these problems may result in bonus points toward your journal grade.

**Prepare the following Journal Homework for class Wednesday, January
25:**

- Read pages 807-809 of Section 12.3 in the text.
- Work/write up problems 1, 11, 14 and 19 on pages 812-3 (Section 12.3).
- Optional problems: 7, 13, 15 and 17 on pages 812-3 (Section 12.3).

**Collected Homework (Due Friday, January 27, 10:10AM):**

- Complete this worksheet. (This is complete now.)
- Be sure to justify your answers. Please staple your work (if more than one page) and use pencil.

**Prepare the following Journal Homework for class Friday, January
27:**

- Read pages 809-812 of Section 12.3 in the text.
- Finish the groupwork sheet we started in class. (You do not need to put those problems in your journal.)
- Work/write up problems 21, 27, 31 (see Example 5), 37 and 55 on pages 813-4 (Section 12.3).
- Optional problems: 23, 25, 47 and 57 on pages 813-4 (Section 12.3).

**Welcome to Multivariable Calculus!!!**

**Remember to keep your appointments!!!**

**Collected Homework (Due Wednesday, January 18, 10:10AM):**

- Write an autobiographical essay as assigned on the syllabus.

**Prepare the following Journal Homework for class Wednesday, January
18:**

- Read the syllabus.
- Read the second half of this website for ideas on how to give a good journal problem presentation. Although this page is directed toward Math 135 students, many of the same ideas apply here.
- Read pages 793-796 in the text (Section 12.1).
- Continue working on the generalization of the distance formula (see page 795).
- Work/write up problems 3 (what does this have to do with projections?) and 7 page 797 (Section 12.1). Remember to follow the guidelines in the syllabus.

**Collected Homework (Due Friday, January 20, 10:10AM):**

- Complete this worksheet. (This is now complete.)
- Be sure to justify your answers. Please staple your work (if more than one page) and use pencil.

**Prepare the following Journal Homework for class Friday, January
20:**

- Start reading Section 12.2 in the text, especially page 798 and the beginning of the part on components (800-801).
- Work/write up problems 11, 13, 27, 29, 33 and 35 on pages 797-8 (Section 12.1). Remember to follow the guidelines in the syllabus.
- Work/write up problem 1 on page 805 (Section 12.2).

Erika L.C. King

Last modified: Mon 1 May 17:10:07 EDT 2006