Instructor: Dr. Shari Ultman
e-mail: shariultman@boisestate.edu
Office: Math/Geoscience Building, Room 236D

Office Hours: MWF 10:30--11:30 (in Engineering Building), and by appointment.

My Weekly Schedule

Teaching Assistants: Alex Hughes and Sami Johnson.
Help Sessions: M 3:00--4:00pm, Tu 12:00--1:00pm, F 4:00--5:00pm (in Engineering Building)

#### Announcements

• Final Exam Information: The final exam will be held in our regular classroom (ENG110) on Monday 17 December from 12:00--2:00. You will be allowed two sides of an 8.5"x11" sheet of paper for handwritten notes, plus all notes used on previous exams, the table of basic derivatives and integrals posted on the course website, and a scientific calculator. The equation sheet will be provided. No other notes or technology will be allowed for this exam.

• Sat 12/14: The grades for this course will be determined by taking the maximum of the two following scores:

• The score computed according to the rubric given in the course syllabus, with the additional provisions that the lowest homework score and the two lowest WebAssign scores will be dropped.

• The score computed by the following rubric:
• Exams: 70% of course grade. If the score on the last exam is higher than at least one of the midterm scores, it will replace the lowest midterm score (this is explained in more detail on the rubric on the course syllabus). Total points possible: 250 points.
• Homework: 10% of course grade. The lowest score is dropped. Total points possible: 60 points.
• WebAssign: 10% of course grade. The two lowest scores are dropped. You can find your current WebAssign grade (with the two lowest scores dropped) on WebAssign. The WebAssign grade appears as a percentage.
• In-class and quizzes: 10% of course grade. This score is computed by dropping the lowest in-class score and the lowest quiz score and adding all remaining in-class and quiz scores. Total points possible: 160 points.

Also: brief solutions to assignment 11.

• Mon 12/10: Computing the curl or divergence of a vector field: compute curl and divergence in rectangular coordinates $(x,y,z)$.

• Sat 12/8: Volume integrals from class, Wed 12/5 (note that there may be other ways of setting up these integrals that works equally well).

• Fri 12/7: The final exam will be held in the room in which our class normally meets.

• Mon 12/3: Grid lines on the paraboloid $z = x^2 + y^2$ polar vs. cartesian.

• Fri 11/16: You can now work on all past-due assignments on WebAssign --- including those from earlier this week (and for the rest of the course). Scoring will be 50% for all problems completed after the original due date for the assignment. You will retain credit for work completed on time. Use the "extension request" link.
Two important notes:
• You cannot get an extension if you have looked at the answer key (this is a feature of WebAssign).
• DO NOT RE-DO CORRECT PROBLEMS: doing so may lower your score (I haven't figured this out yet --- I'll let you know if I do.) I WILL NOT RE-SCORE ASSIGNMENTS DUE TO ACCIDENTAL RE-ENTERING OF (PREVIOUSLY CORRECT) ANSWERS.

• Sat 11/10: As we move into the last month of the semester, I want to encourage students whose grade estimates are below 75% to take some time to speak with me about strategies for improving their grades. My Monday office hour is canceled, but I will have regular office hours on Wednesday and Friday. In addition, I plan to be in my office next week at the following times:
• Monday 11/12: 12:30--3:00
• Tues 11/13: 12:00--2:00
• Wed 11/14: 12:00--3:00
• Thurs 11/15: 2:00--4:00 (Apologies for canceling --- I double-booked myself.)
Feel free to drop by.

• Fri 11/9: An estimate of corse grades (as percentage) as of 11/8 have been posted on BlackBoard. Scores used in these computations are: midterm exams 1--3, in-class response 9/5--11/7, quizzes 1--5, homework assignments 1-8 and WebAssign assignments 1--23. The grading rubric can be found on the course syllabus. If you would like to experiment with how various scores on midterm 4 and the final exam will affect your grade, you can download this .xls spreadsheet.

• Wed 11/7: More on volume elements in cylindrical and spherical coordinates at the Bridge Book. Note the difference in notation; in the Bridge Book, both cylindrical and spherical radii are represented by $r$, the polar angle is represented by $\phi$, and the angle of declension in spherical coordinates is represented by $\theta$.

• Mon 11/5: The problem from class today is due at the beginning of class on Wednesday: set up the triple integral in cylindrical coordinates that gives the volume of the region below the paraboloid $z = 4 - x^2 - y^2$ and above the cone $z = \sqrt{x^2 + y^2}$. Use the order of integration $dV = r\, dz\, dr \, d\theta$. You may work in groups; if you do, make sure the names of all members of your group appear at the top of the page. (You do not need a coversheet for this one.)

A note on terminology. If a region is "bounded below" by a curve (or surface), then the region lies above the curve (or surface). Similarly, if a region is "bounded above" by a curve (or surface), then the region lies below. This was the way the problem from Friday was described (see below). Today's problem is describes the region as lying below one surface and above another. You will find both forms of description used with pretty much equal frequency.

• Fri 11/2: The problem from class today is due at the beginning of class on Monday: use polar coordinates to compute the integral $\iint_R xy \, dA$, where $R$ is the region in the first quadrant of the $xy$-plane bounded below by the curve $y = \sqrt{2}$ and above by the curve $x^2 + y^2 = 4$. You may work in groups; if you do, make sure the names of all members of your group appear at the top of the page. (You do not need a coversheet for this one.)

Remember to change clocks on Sunday.

• Mon 10/29: I've reviewed WebAssign assignment #20 --- I'm going to keep the due date as Wednesday 10/31. The material we covered today in class is sufficient for you to tackle these problems, especially in conjunction with the "practice another problem" and the examples given in the book. Two tips:
• For problems #4,5: when switching order of integration, first draw a picture of the region based on the limits of integration in the original integral.
• For #8: Average height is "total height" (the integral of H over the region R) divided by the area of R.
• The area of $R$ is the integral $\iint_R dA$: the integrand is the constant function (no units). Think "chop and add". The region $R$ is chopped into small pieces of area; integrating "adds up" all these small areas to give total area.

• Tues 10/23: If you have a laptop, bring it to class on Wednesday 10/24 --- we may begin working on WebAssign assignment #19 (method of Lagrange multipliers) together. Also, I will be in my office (MG 236D) from noon to 3:00 on Wednesday; you can come by to ask questions, and/or to pick up old homework assignments, exams, etc.

• Mon 10/22: Assignment #7 covers sections 14.7 and 14.8, not sections 14.6 and 14.7. This has been corrected on the "Homework" page. A hint for problem #35 in section 14.7 --- look at example 5 on page 838.

• Fri 10/19: Multiple announcements:
• One of your colleagues pointed out to me that this text treats the object $D_{\vec{v}}f = \vec{\nabla} f \cdot \vec{v}$ as a category of derivative in it's own right --- be advised that this is (in my experience) non-standard. This being the case, however, I will allow the answer "true" to Question #5 (the $\hat{v}$ should have been an indication that the derivative in question was a directional derivative, but I realize that it was difficult to see).

• Another of your colleagues pointed out a typo on the last of the additional problems on homework assignment #6, turned in this morning. This was the chain rule problem involving a box whose sides are changing with time. This problem will not be graded. I will repost a corrected version of this problem to be turned in next Friday 10/26: it will be worth 1 point extra credit (added to assignment #6).

• I remembered after class ended that there is a homework assignment ready to be returned. I forgot to run by my office to grab it on the way to class. If you want to stop by my office (MG236D), you can pick it up this afternoon from 12:30--3:00pm.

• I have been approached by several students requesting to be allowed to re-schedule the next exam. You can not reschedule an exam unless i have an official letter from your coach. Please be sure to get me such a letter *before* the exam, or you will *not* be allowed to take a make-up exam. If you gave me an official letter at the beginning of the semester, you are covered and do not need to bring me another letter.

• Wed 10/17: There seems to be confusion over the difference between the linear functions $L(x,y)$ and $\Delta f(x,y)$:

• $L(x,y) = f_x(a,b)(x-a) + f_y(a,b)(y-b) + f(a,b)$ is the "local linearization", the linear function that best approximates the value of the function $f$ --- that is, $f(x,y) \approx L(x,y)$ for $(x,y)$ "near" $(a,b)$.

• $\Delta f(x,y) = f_x(a,b)(x-a) + f_y(a,b)(y-b)$ approximates the change in the value of the function $f$ between the points $(a,b)$ and $(x,y)$ --- that is, $\Delta f(x,y) \approx f(x,y) - f(a,b)$ for $(x,y)$ "near" $(a,b)$. It may be useful to observe that $\Delta f(x,y) = L(x,y) - f(a,b)$.

• In both of the above cases, $(x-a)$ is often represented by $\Delta x$, and $(y-b)$ by $\Delta y$.

• Just for good measure: the differential $df = f_x dx + f_y dy = \vec{\nabla} f \cdot d\vec{r}$ can be thought of as reflecting the change in the function's value when $\Delta x$ and $\Delta y$ are small ($\Delta x$ has been replaced with the differential $dx$, and $\Delta y$ with $dy$).

Hint for problems #41 & #46, section 14.5: the gradient of a function is orthogonal to the level sets of the function. In both of these problems, represent your surface as a level surface of a function in three variables. See example #11, p. 822. Level surfaces are defined on p.782.

• Mon 10/15: This week's homework assignment is posted in its totality. Note that there are "additional problems" assigned this week.

• Fri 10/12: No additional WebAssign posted this weekend -- so the only WebAssign assignment due Mon 10/15 is #15. There are, however, "Additional Problems" posted with homework assignment #6 -- these problems involve using the differential to analyze changes in functions due to small perturbations in the domain.

• Assignments #13 and #14 should now give you the solution once you have maxed out your attempts. It should also be marking you submissions as correct or incorrect (green check/red x respectively) after each submission. Please let me know if this does not happen.
• The due date for Assignment #13 has been rescheduled for Wednesday 10/10 at 8:45am, and two extra submissions are now allowed on this assignment (total of 7 each).
• The due date for Assignment #14 is still Wednesday 10/10 at 8:45am.

• Thurs 10/4: WebAssign assignment #13 has been posted. It is due on Monday 10/8.
• The purpose of this assignment is for you to learn how to compute the partial derivatives of a function of two or more variables.
• Computing the partial derivatives of a multivariable function is a Jedi mind trick: they are computed exactly like "regular" derivatives (that is, the derivatives of functions of a single variable you learned in Calc. I), while treating some of the variables as though they were constants. Read the sentence immediately preceding example 1 (p 794), and look at examples 1--4 (pp 794--796).
• If you need extra practice with regular derivatives, work on problems in the WebAssign assignment "Differentiation Review" (this is for practice only; it is not worth any points).

• Wed 10/3: The example from class today, and some visuals: An online graphing resource: Barbara Kaskosz's Surface/level curve grapher applet. Let me know if there are other online surface and/or level curve graphers you use, and I'll add them to the "links" page.

• Mon 10/1: WebAssign assignment #11, due Wednesday 10/3 at 8:45am, has been posted. NOTE: for this assignment, you are allowed only 3 attempts per question, not the usual 5 attempts per question. Also: TA help session for Monday 10/1 and Tuesday 10/2 have been canceled; my office hours for Monday 10/1 have been canceled.

• Sat 9/30: Important equations. As with the review, one point extra credit on the exam to the first person to correctly identify and e-mail me about typos.

• Fri 9/28: We did not get through as much of the example in class today as I was hoping. If you are interested in seeing the entirety of the planned examples, they are here (with notes). The slides from today's quiz are here.

• Wed 9/26: The review for the second exam has been posted. Also, the due date for WebAssign assignment #10 has been rescheduled --- it is now due on Monday 1 October at 8:45am.

If you go to the "Notifications" link (top right corner of your WebAssign page) and check the box "Notify me immediately when...my instructor responds to a help request", you will be automatically sent e-mail when I have responded to your "Ask My Teacher" request. This is also a good time to check that you are receiving reminders for due assignments, and notifications when a due date changes or an announcement is posted (I'm using the WebAssign announcements to send out automatic e-mails when I add assignments to WebAssign).

This is a new feature for me, so if you don't receive a response to an "Ask Your Teacher" request within a reasonable amount of time (say, 12 hours), please e-mail me.

• Mon 9/24: Here's a research fellowship opportunity for undergraduates at BSU.
Also: the grades on BlackBoard have been updated, including a corrected score for quiz 1 (there was a spreadsheet error in the grades originally uploaded -- most people's scores should now be a bit higher than before).

• Sat 9/22: One more announcement regarding the retest on Monday. You need to bring your original exam, so I can make sure you get proper credit on the retest.

• Fri 9/21: Several announcements:
• The retest will be held on Monday 24 September at 8:15am. If you cannot make this time because of scheduling problems, you must let me know no later than 9:00am Saturday the 22nd; I will be in e-mail contact with you over the weekend to arrange an alternate time on Monday. Details about the re-test:
• Material from problems 1--3 will be re-tested. Reason: this material is absolutely fundamental to this class. This re-test is an attempt to encourage students who do not understand this material to revisit it before we move on.
• You can only get credit for problems you missed on the original exam.
• You can recover up to 75% of the original point value (so, a 4 point problem on the exam will be worth 3 points on the re-test).
• You may not use notes.
• There will be no partial credit.
• A student's solution manual is now on reserve at the library, in addition to two copies of the course text. These are for use in the library only.
• Statistics for the first midterm have been posted on the "Exams" page.
• Grades for everything except WebAssign should now be visible on BlackBoard. Please take a moment to check and make sure I have entered your scores correctly. If you find a problem, or cannot access your grades, please let me know.

• Mon 9/17: Several announcements:
• IMPORTANT: Make sure your clicker is registered on BlackBoard. Today, there were approximately ten responses from clickers without names associated with them. You will not receive credit unless your clicker is registered.
• I've opened a new thread on the "WebAssign Issues" forum on the BlackBoard discussion board. The thread is titled: "Entering trig functions." If you have had difficulties getting WebAssign to accept your trig functions, please visit (better yet, contribute to!) this thread.
• Here's a nice piece exploring unit analysis. Also, don't forget that the 22nd First Annual Ig Nobel Prize Ceremony is this Thursday.

• Fri 9/14: Homework is graded out of six points total. If you get a "6", you get full credit.
• On the first assignment, points were taken off only for a substantial number of missing problems, or for serious breaches of formatting. In the future, points will be awarded according to the rubric posted on the homework page.
• Notes and solutions to some of the problems on today's worksheet have been posted.

• Sat 9/8: Instructions for viewing past assignments on WebAssign (courtesy of Derek Eichelberger -- thank you!) can be found here.

• Fri 9/7: Two copies of the course text have been put on reserve at the library. They can be borrowed for up to two hours. Also, a reminder that Alex and Sami will have help sessions in the Engineering Building today from 4:00--5:00, Monday from 3:00--4:00 and Tuesday from 12:00--1:00. Finally, You may already know this, but...you can have WebAssign send you e-mail notifications reminding you of due dates, telling you if there are changes to an assignment, etc. Click on the "notifications" link on WebAssign.

• Wed 9/5: Two new discussion forums have been created on BlackBoard: a study group forum, and a forum for discussing technical issues with WebAssign. I am subscribed to all forums.
Also, the class schedule has been updated. This does not affect the homework or the WebAssign assignments.

• Sun 9/2: Please check WebAssign. WebAssign assignment 2, due Wednesday 5 September at 5:01pm, has been added (I thought this had been done before class on Friday, but for some reason, it seems not to have been added then).
Also, WebAssign assignment 3, due Friday 7 September at 8:00am, has been added. Note that this assignment will include basic computational problems from section 12.4. Although we will not cover this section until class on Friday -- after the assignment is due -- these problems are simple enough that you will be able to figure them out using the text and the hints from WebAssign. All the information you need is on p.688. You may also, if you wish, use the properties listed in Theorem 2, together with Equations 5 (all on p.690), but this is not necessary.

• Fri 8/31: Two Three announcements:
• Here is the worksheet on parametrizing lines from today's class.
• To check whether your clicker is properly registered and is working, go to "Course Documents" on BlackBoard and look at the .pdf file posted under "Second (and last) clicker check".
• If you are interested, here's an internship opportunity through the Idaho National Lab.

• Wed 8/29: Notes on problems #57 and 58 in section 12.1 (homework assignment 1). The answer to problem #57 in the back of the textbook is incorrect. Also, for problem #58, use units of pounds instead of kilograms.

• Wed 8/29: To check whether your clicker is properly registered and is working, go to "Course Documents" on BlackBoard and look at the .pdf file posted under "Clicker check".