Calculus III (MAC 2313) — Spring 2017

Instructor: Christopher Stover (webpage)
Email: cstover (at) math (dot) fsu (dot) edu
Office: MCH 402F
Office Hours:
Wednesdays  ‐ 12:00pm to 1:30pm;
Fridays ‐ 1:30pm to 3:00pm;
or by apponitment (!!!)
Meeting Location: 106 LOV
Meeting Times:
Mondays & Wednesdays ‐ 5:15pm to 6:05pm
Tuesdays & Thursdays ‐ 5:15pm to 6:30pm
Final Exam:
Wednesday, May 3, 5:30pm to 7:30pm
Syllabus: .pdf
Required Text:
Calculus: Early Transcendentals, 7th Edition, by James Stewart. (Amazon)
Supplementary Resources:
  • Slack Show Details

    Slack is an organization-centered chat tool that allows largescale collaboration, discussion, and interaction. Think of it as a chat room on steroids!

    While I'll always be available (unless otherwise noted) during office hours and via email, Slack will allow evveryone the opportunity to chat with me + other classmates, both in real-time and asynchronously. It's an extremely valuable resource!

    Slack can be used directly from any Internet browser. Our class's room info is:

    To get started, you should:

    1. Navigate to the signup page
    2. Enter your 
      my.fsu.edu
      email address; make sure you're able to check the email address you enter or else you'll miss any confirmation emails, etc.
    3. When you choose a username, please choose one that I'll be able to recognize! Sometimes, assignments include (graded) 
      Slack
      components, and you probably don't want to miss out on a grade because I don't recognize you as duckface_brah_doo_1993_lululz or something similar!
    4. Feel free to email me at any time if you have trouble signing up.

    Note: Slack can be used directly from any Internet browser with no installation needed. However, you can also install it on any computer, phone, tablet, etc., so that you have access to our course chat at all times. For more information about installing Slack, see: https://slack.com/downloads.

  • Blackboard Show Details

    I'll make use of Blackboard for announcements, sharing of documents, and gradebook maintenance. My goal is to keep this webpage synced up with all of that data except the gradebook, however, so by and large, you likely won't need to check both this site and the Blackboard page.

    As of now, you should all be added to the Blackboard site automatically. If you're not sure how to find it, you should:

    1. Navigate to MyFSU.
    2. Sign in with your FSU username and password.
    3. Click on the BlackBoard icon in the left column.
    4. Locate course number 
      MAC2313-0009
      under FSU Class Schedule.

  • Web Assign Show Details

    WebAssign is an online homework and grading system used in various courses at FSU. It contains problem sets for which students can receive immediate feedback as well as an online copy of the textbook.

    For our class, the WebAssign problem sets will be additional practice which will not be directly factored into the homework/quiz portion of your final grade. However, you should note that:

    • Doing lots of problems is a proven way to succeed in math courses, and WebAssign will provide that opportunity along with instant feedback.
    • WebAssign will be a convenient tool for me to use to pick problems to put on homework/quizzes/exams. For that reason, the more problems you do on WebAssign, the more familiar you'll be with stuff I'm likely to give you later.

    You can access WebAssign directly from our Blackboard site:

    Alternatively, you can log in directly from the WebAssign login page using your username (presumably, your 
    my.fsu.edu
    user name), our institution code (
    fsu
    ), and your password (whatever you chose for that). If you forget your password, you can reset it here: WebAssign Password Reset.
Below is a calendar highlighting the important dates for our class this semester. To access it from a web browser and/or to import it into your personal apps, use the HTML and/or iCal link(s):   HTML Link   –   iCal Link
Homework 2: Handout   Solutions
Homework 1: Handout   Solutions

Corrections:

5(g): Here, $\mathbf{w}$ is another arbitrary vector in $\mathbb{R}^3$ which should have been included in the directions. To proceed, let $\mathbf{w}=\langle w_1,w_2,w_3\rangle$ and complete the proof of the identity.

6(g): For some reason, I wrote the equation of a plane rather than the equation of the line I actually asked about! Hah!

The line in question is parallel to the cross product of $\vec{PQ}\times\vec{PR}=\langle -1, -1, -1\rangle$ and contains the point $P(0,1,0)$, which means we have $x=0-t$, $y=1-t$, and $z=0-t$, i.e. $x=-t$, $y=1-t$, and $z=-t$.
Final Exam Info
Logistical Info about the Final: .pdf
Vector Calculus
16.7–16.9 Review Problems: .pdf   Solutions

Corrections:

2(ii): In the solutions, I incorrectly wrote the parametrization $\mathbf{r}(x,y)$ with bounds $0\leq x\leq 2$ and $0\leq y\leq 2$. Given that $z$ is a graph (namely, $z=2-x-y$), these bounds imply that the projection to the $xy$-plane would be the $2\times 2$ square. This is clearly incorrect.
     Instead, when we project that triangle to the $xy$-plane, we get the line $y=2-x$ (by solving $z=2-x-y$ when $z=0$). This means that the correct parametrization is the same vector $\mathbf{r}$ with one of the following bounds: Either $0\leq y\leq 2-x\text{ and }0\leq x\leq 2$ or $0\leq x\leq 2-y\text{ and }0\leq y\leq 2$. As a result: The correct answer is $-8$.

3(b): In the solutions, I said highlighted the vector $\langle -1,-1,-1\rangle$ (inside the integral) and said "...plugging $\mathbf{r}$ into $\mathbf{F}$ doesn't change $\mathbf{F}$." That should say: "...plugging $\mathbf{r}$ into $\operatorname{curl}(\mathbf{F})$ doesn't change $\operatorname{curl}(\mathbf{F})$," and this is true because $\operatorname{curl}(\mathbf{F})=\langle -1,-1,-1\rangle$ is a constant vector. For example, if $f(x)=3$, then plugging $x=7$ into $f$ still yields $f(7)=3$; similarly here, $\operatorname{curl}(\mathbf{F})=\langle -1,-1,-1\rangle$ implies that $(\operatorname{curl}(\mathbf{F}))(\text{anything})=\langle-1,-1,-1\rangle$ because there are no variables to plug $\text{anything}$ into.
Multiple Integrals
Exam Review: .pdf   Solutions (note: this is a 3.4 MB scan, i.e. ~25x larger than the other answer keys!)

Corrections:

3(c): The $\theta$ range should be: $\frac{\pi}{4}\leq\theta\leq\frac{3\pi}{4}$.

5(b): If you try to follow the kind of but not really cylindrical note on the answer key, there's a typo: The innermost integral should be $\int_{-1}^{4-r\sin{\theta}}$ rather than $\int_{-1}^{4-r\cos{\theta}}$. Both give $20\pi$ as answers.
Multivariable Functions
A Q&A Guide to Concepts You Need to Know: .pdf
Vector-Valued Functions
Exam Review: .pdf   Solutions
Formulas: .pdf
Stuff You Need to Know from Calculus!: .pdf
Vectors
Cross Products: .pdf
Exams
Exam 4: .pdf   Solutions
Exam 3: .pdf   Solutions
Exam 2: .pdf   Solutions
Exam 1: .pdf   Solutions
Quizzes
Quiz 5: .pdf   Solutions

Corrections:

2: The answer I wrote should be multiplied by 2 to get the right answer. Here's why:

Recall that $\iint_Df(x,y)dA$ gives the volume of the solid bounded between the region $D$ (in the $xy$-plane) and the function $f(x,y)$.

However, you're asked to find the volume of a region that is half above the $xy$-plane and half below it (the $xy$-plane is in green):

As such, the volume I've written here is for the top-half, and to get the total volume, we have to multiply by 2.

5: This isn't entirely correct; there are two different ways to fix it.

  • In the problem, use the plane $z=0$ instead of $z=1$; or
  • change the region $D$ so that $1/\sqrt{3}\leq r\leq 1$.

I'll try to get a properly drawn/answered version posted here soon; sorry for not catching this sooner!
Quiz 4: .pdf   Solutions
Quiz 3: .pdf   Solutions
Quiz 2: .pdf   Solutions
Quiz 1: .pdf   Solutions
Miscellaneous Handouts:
First-Day Handout: .pdf
My Schedule: .pdf
Chapter 16 Hide
Section 16.9: Notes
Problems: (1-15)(!!!); 17-18; (23-32)*
Section 16.8: Notes
Problems: (1-10, 13-15)(!!!); (16-20)*
Section 16.7: Notes
Problems: (5-32)(!!!)
Section 16.6: Notes
Problems: 3-6, 13-26; (33-36, 39-50)(!!!)
Section 16.5: Notes
Problems: (1-8, 12, 13-18, 23-29)(!!!); 19-22, 30-32; (33-39)*
Section 16.4: Notes
Problems: (1-14)(!!!); 17-18; (21-31)*
Section 16.3: Notes
Problems: (3-10, 12-20, 31-34)(!!!); 23-24, 28-30
Section 16.2: Notes
Problems: (1-16, 19-22)(!!!); 17-18, 29(a), 30(a), 32(a); (33-50)*
Section 16.1: Notes
Problems: 1-18, 29-32; (21-26)(!!!)
Chapter 15 Show
Section 15.10: Notes
Problems: coming soon
Section 15.9: Notes
Problems: coming soon
Section 15.8: Notes
Problems: 1-12, 15-16; (17-26, 29-30)(!!!)
Section 15.7: Notes
Problems: 1-2, 19-22, 27-28, 55; (3-22, 29-36)(!!!)
Section 15.6: Notes
Problems: (1-12)(!!!); (17-24)*
Section 15.5: We skipped this section
Problems: No problems
Section 15.4: Notes
Problems: (1-14, 19-27, 29-32)(!!!); 15-18, 33-34; (37-41)*
Section 15.3: Notes
Problems: 1-16, 43-54; (17-32odd)(!!!); (55-58, 63-67)*
Section 15.2: Notes
Problems: 1-14, 25-31; (15-22)(!!!)
Section 15.1: Notes
Problems: 1-4; (11-13)(!!!);
Chapter 14 Show
Section 14.8: Notes
Problems: 3-12, 15-21; (29-41)opt
Section 14.7: Notes
Problems: 1-4, 5-18 odd, 29-36, 39-49 odd; (19-20, 50-56)*
Section 14.6: Notes
Problems: 4-17, 19-26; (41-46)opt; (27-29, 37-40, 49-68)*
Section 14.5: Notes
Problems: (1-14, 17-34)(!!!); (45-59)*
Section 14.4: Notes
Problems: (1-6, 11-16, 25-32)(!!!); (17-18)opt; (42-46)*
Section 14.3: Notes
Problems: 15-70 odd; (1-14)opt; (71-72, 75-81, 87-89, 93-101)*
Section 14.2: Notes
Problems: 5-22, 25-26, 29-38; (39-46)*
Section 14.1: Notes
Problems: 9-33, 38-50, 65-68; 32, 59-64(!!); (69-70)*
Chapter 13 Show
Section 13.4: Notes
Problems: 3-16, 37-42(!!!)
Section 13.3: Notes
Problems: 1-6, 10-12, 17-29, 47-50; (30-31, 38-39, 43-45, 53, 55-63)*
Section 13.2: Notes
Problems: 3-26, 29-31, 35-40; (41-56)*
Section 13.1: Notes
Problems: 1-14, 27-30, 40-44; (15, 16, 21-26, 47-49)*
Chapter 12 Show
Section 12.6: Notes
Problems: 21-28(!!!); (3-8, 11-20, 29-36)opt
Section 12.5: Notes
Problems: 1-40 odd, 48, 50, 51-74 odd; (75-82)*
Section 12.4: Notes
Problems: 1-36 odd; (37, 38, 42-53)*
Section 12.3: Notes
Problems: 1-44; (45-48, 61-64)*
Section 12.2: Notes
Problems: 1-26; (27, 41-52)*
Section 12.1: Notes
Problems: 1-34; (35-38)*
* = hard problems
(!!!) = extremely important
opt = optional
Good supplementary resources for multiple integration: Dummit

Dummit's notes are really good, especially the part on changing the order of integration in triple integrals (see the example on pp 10--12 for a really good explanation)!
Why $dy/dx$ is kinda sorta a fraction but not really: 1 (!!!)  2  3  4  5  6

And similar stuff about differentials $dx$, $dy$, etc.: 1  2  3  4

...and other related things about $d/dx(y)$ and $dy/dx$ about how $dy/dx(dx)=dy$ and...: 1  2  3
What is a determinant?! 1 (not good)  2 (not good)  3 (some good, some not)  4 (the best)

Note: "The best" answer also another suggests why wedge products (which I mentioned in class on Jan 17 as a "more logical version" of cross products) should be taught in/around Calc 3 instead of wayyyyyy later, as is currently the pedagogical norm.

A short, geometrical interpretation: The determinant of a square matrix is the (oriented) volume of the (hyper-)parallelepiped spanned by its column vectors. This comes from the (wonderful!) introduction to differential forms found here.

An axiomatic treatment can be found on page 33 (Definition 3.1) of the above-linked .pdf.
Why does the determinant have the form it has?! 1 (some good, some not)

But why does it alternate plus and minus?! That's because of cofactors! As it happens, wedge products are also a good way to understand these!

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