Math 213
Multivariate Calculus

Syllabus, Mayterm (2022-) 2023

I'm planning for us to meet in person. Traditionally we meet at 8:30-10 am and 10:30-noon.

Our first day will be at 9:00 am, Wednesday May 3, 2023, Tentatively in: Newcomer Center NC 12. We'll meet 9:00-10:00 and 11:00-noon

Prerequisite: Math 211 (Calculus I) completed with a grade of C or better.

Professor Paul Meyer Reimer
Sci 011 · +1.574.535.7318 (ofc)
paulmr@goshen.edu · +1.574.312.3395 (cell)

I don't have fixed office hours. You are welcome to stop by my office (SC 011) any time! Here's my teaching schedule this term,

If you are off campus and want to make sure I'm available before coming to campus You may e-mail or text me to make a time to get together.

Do not worry that you're "bothering me" when you stop by! Every time a student stops by it makes a good impression on me, and I think "Oh, they are taking charge of their own learning, and are taking the class seriously!".

Text / course materials

Active Calculus - Multivariable by Steven Schlicker, with David Austin and Matthew Boelkens. We'll cover the whole contents of this textbook.

This is a Creative Commons licensed (free!) open source textbook. You may download a .pdf of the textbook, or refer to the online version (.html) from any computer.
Calculus volume 3 by Gilbert Strang. Also an open source textbook. We'll use this textbook for studying Div / Grad / Green's Theorem.
Your GC - issued iPad.
Class website: tiny.cc/gc-calc3
with a general schedule, course documents, lecture notes. Follow the link and then bookmark (on your iPad) the site at people.goshen.edu:
A stylus for your iPad. Any cheap one (~\$10) one should work. You do not the snazzy (10$\times$ \$10) apple pencil. But it will also work.
Notability, an iPad app. I am hoping this has been automatically installed on your iPads already! Using Notability and a stylus, you can easily download sections of our open-source textbooks, or any .pdf, and take notes or work on problems "on top of" the text, that you can save and return to later.
We'll be using Edfinity as our homework system.
You can purchase a registration code directly from Edfinity (\$25) or from the Goshen College Bookstore (somewhat more expensive).
But if your financial aid package includes books you *must* go through the Bookstore to purchase access to take advantage of that financial aid.
Our course name in Edfinity is (Math) 213 MV Calc III @ GC • May 2023. To enroll:
- If you already have an Edfinity account from a previous course, please sign into it and search for our course.
- Otherwise:
  1. Go to edfinity.com/join/7BPVCKHP
  2. You will be prompted to pay and enroll in our class.
Grades and reading questions: on moodle.goshen.edu.
CoCalc Sign up for an account with your *@goshen.edu e-mail! We'll use Jupyter notebooks for labs, and they're a useful calculation aid at any time! Signing up for an account is free.
GeoGebra geogebra.org/3d is software for 3-d plotting / parametric plotting / 3-d visualization. Sign up for a free account. We'll be using this for in-class activities and labs.

You can also download and use the free GeoGebra iPad app. May be faster than the website at times? It promises you can save and share your work, but I haven't tested that feature.
We may use Desmos (2-d graphing), and WolframAlpha [the paid WolframAlpha app has been available on your GC-registered iPad for free through the GC App Catalog], and perhaps others.

Course Objectives

The core concepts / techniques of multivariate calculus include: vectors and vector operations, vector-valued functions, functions of several variables, partial differentiation, double- and triple-integration, vector fields, line and surface integration, and vector analysis.

You will be able to:

describe and use the core in analytic, numeric, graphic, and verbal contexts.
solve pure and applied problems.
use computer software to investigate and visualize the core, and solve multivariate calculus problems.
learn mathematics effectively by reading a textbook, completing exercises, collaborating with peers, and interacting with an instructor.
communicate mathematics effectively in writing and conversation.

Class activities, attendance, study

To get an *average* grade in a 4-credit hour course, you should expect:

semester		May term
54 hours in class + 108 hrs out =	162	= 47 hrs in class + 115 hrs out

Our class is *very* concentrated: Spreading this out over the May term, each day we'll meet for 3 hours, and you should count on spending 7 hours out of class on reading, assignments, and study. That's a lot of Calculus! That's a full time job! Make sure you take some breaks, and use weekends both for some study and some relaxation.

You are expected to attend class every day and to actively participate in class activities. You are expected to come prepared. This means that you should have read the book and be prepared to ask questions about the reading and the problems you are asked to do. You should be prepared to do problems and take part in class discussions and in class problem solving. Attendance is reflected in the 'participation' part of your semester grade.

See the page on Math-do, The way of math for more concrete suggestions.

Grades

homework / reading questions / labs	15%
2 videos of core skills problems	10%
exams	21%$\times$3=63%
best of (exam 1 \| 2 \| 3 \| top 2 core videos)	9%
participation	3%

minimum grade outcomes:

I may adjust this scheme down a bit (e.g. 89% might end up being good enough for an A), but I certainly won't adjust it up.

Grades are intended to reflect the degree to which the mathematical content has been mastered - not the performance of one student in relation to others.

If you have reason to drop this course, be sure to check the deadline for doing so. If you think you need to receive the "I" (incomplete) grade, you must see me to discuss this option. An incomplete will not be automatically given.

Exams

The three exams are cumulative in the sense that material in later sections assumes understanding and knowledge gained from previous sections. Exams can only be rescheduled or made up under very unusual circumstances. You'll need written documentation and should let your instructor know ahead of time or as soon as possible thereafter.

Videos of 2 core problems

You'll solve 2 designated problems on "core" skills, and make a video talking through your solution to each problem. Here's more information, and an example video.

Collaboration

You are encouraged to use all available resources in order to learn the concepts and techniques discussed in this course. In particular, conversations with other students and the instructor can be an effective learning method. Reading other books and web pages can be another effective learning method. However, copying someone else's work subverts the learning process.

For assignments, look at and discuss each other's work. But see if you can hide all such work and still work solutions on your own. You can't do this on webassign, but on other written work developed during collaboration with another student, give them a shout out, writing a brief acknowledgement (just as you should cite any sources you use in all your written work at college).

For exams, of course, you may not use any resources unless a specific exception is stated by the instructor.

Participation

Come to class prepared and ready to ask questions about readings, homework and other assignments..

The participation portion of your grade will reflect unwarranted absences (more than 2), as well as your engagement with class activities.

Attendance

Go to class! Seriously, unless you are half dead, go!

- Megan Taylor, Salem College, ’15

Class attendance is important. Don't miss out!
But things will come up in the rest of your full lives. You do not need to give me an excuse if you miss class once or twice.
If you know ahead of time that you will miss a class, let me know ahead of time.
If you find yourself struggling in class, 2 absences will be too many.
It is always your responsibility to find out what you missed. Class notes are usually available for you to review. But you should also also ask another student who was present or ask me what you missed that may have not made it into the notes.
For classes I teach with a lab component: Don't lightly miss any labs! Absence from labs impacts not only you, but also your lab partner who might be waiting to start / finish an activity if you don't show. If you must miss any lab time, you must communicate with both your lab instructor and your lab partner(s) ahead of class.

Beyond 2 absences I'll expect a note explaining your unavoidable absence and/or a conversation--It's best if you've intiated the conversation!--about the barriers that you're facing to attendance, so that we can brainstorm some solutions or connect with outside resources to reduce/eliminate those barriers.

Community Activities (CA)

2% of your grade in all the classes taught through the physics department is credit for your engagement in community activities. You may earn up to an additional 2% extra credit. See the Community Activities website.

Collaboration and Academic Integrity

You are encouraged to use all available resources in order to learn the concepts, skills, and content of this course.

Talk with other students and the instructor!
Form study and homework groups!
Discuss with others promising approaches to problems!
Go to the library and find books!
Ask a librarian for help in finding resources!
Find useful web pages!

Collaboration, and building on the works of others are how almost all academic work by professors, researchers, students, writers gets done.

However, simply copying someone else's work sabotages your own learning and hides the truth about what is your work and what is the work of others. So, it must be clear in everything you write and turn in what is your work and what is someone elses.

Academic Integrity

Academic dishonesty is any act that misrepresents your academic work or interferes with the academic work of others. Examples of academic dishonesty include, but are not limited to, the following: cheating on assignments or exams, falsification of data, submission of the same or similar paper without professor consent, depriving others of academic sources, or sabotaging the work of another. Academic dishonesty also includes submitting someone else's assignment as your own or helping someone else commit academic dishonesty.

Plagiarism is the use of someone else's ideas or words (sentences, clauses, distinct phrases or calculations) without quotation or citation. you have any questions about what constitutes plagiarism, please ask. Assignments in this course may/will be submitted to Turnitin, which detects borrowed material and generates a "similarity report", for assessment of assignment originality, along with a probability report of AI generation.

The use of artificial intelligence (such as ChatGPT) to complete assignments is also considered plagiarism when it misrepresents work as a student’s own words and ideas. In some cases, professors may allow or even require the use of AI for instructional purposes. Such exceptions apply only when a professor has given explicit permission to use these tools.

In this, as in any college class, you can protect yourself from charges of plagiarism by acknowledging your sources. This can take the form of the URL of a site you found useful, or a shout out to a classmate who helped you on a particular problem.

Academic Success Center

The Academic Success Center offers tutoring and writing assistance for all students. For further information please see www.goshen.edu/studentlife/asc.

Accessibility Accommodations

Goshen College is committed to providing all students equitable access to programs and facilities. Students who need accommodations based on disability should contact the Academic Success Center (ASC). Students must register with the ASC before faculty are required to provide reasonable accommodations. For more information or to register, please contact the Director of Academic Success, Michelle Blank, Good Library 112, mblank@goshen.edu or 574-535-7526. To ensure that learning needs are met, contact the ASC the first week of classes. More information at: goshen.edu/campuslife/asc/disability-services.

Schedule & Topics

"🚫" means a topic not covered in this term's incarnation of the course.


3 May Wednesday First day: 9:00 am, Newcomer 12	Video homework problems Math-dō Chapter 9 - VECTORS and ANALYTIC GEOMETRY - Learning objectives Multi-variable functions, 3-D coordinates, distance [9.1]
4 May Thursday	MV functions: domains and traces / contours [9.1] Vectors [9.2] Dot product (scalar product) [9.3] Notability
5 May Friday	Cross product (vector product) [9.4] Lines and planes [9.5]
8 May Monday	Vector-valued functions [9.6] Derivatives and integrals of vector functions [9.7] Arc length [09.8]
9 May Tuesday	Curvature [09.8] Chapter 10 - DERIVATIVES - Learning objectives Limits and Continuity [10.1] Partial derivatives [10.2]
10 May Wednesday Test 1	2nd order partial derivatives [10.3] Clairaut and cross derivatives [10.3] Tangent planes and differentials [10.4]
11 May Thursday	Chain rule [10.5] Gradient and directional derivatives [10.6]
12 May Friday	Optimization [10.7] Constrained opt: Lagrange mult [10.8] Chapter 11 - INTEGRATION - Learning objectives Double integrals over rectangular areas [11.1]
15 May Monday	Iterated integrals [11.2] Area between curves [11.2+] Double integrals - general regions [11.3] Check-In survey results
16 May Tuesday	Polar Integrals [11.5] Parametric surfaces [11.6] Surface area [11.6+]
17 May Wednesday Test 2	Triple Integrals [11.7] and Volumes Cylindrical and Spherical Coordinates [11.8]
18 May Thursday	Chapter 6 - VECTOR CALCULUS - Learning objectives Vector Fields [6.1] Landscapes and gradient fields [6.1] Triples...in cylindrical and spherical coordinates [11.8+]
19 May Friday	Gradient Fields [06.1] Scalar Line Integrals [6.2] Vector Line Integrals [6.2]
22 May Monday	Fundamental Theorem: Conservative Vector Fields [6.3] Curl and Divergence [6.5]
23 May Tuesday	Fundamental Theorem: Green's Theorem [6.4] Stokes' Theorem [6.4] Line Integrals SUMMARY
24 May Wednesday Please fill out a course evaluation (before Wed, midnight). Test 3

Image credits

University of Montana Flight Lab

Math 213 Multivariate Calculus