SUNY Geneseo Department of Mathematics
Spring 2018
Prof. Doug Baldwin
Last modified January 28, 2018
Time and Place: MWRF 1:30 - 2:20 PM, Sturges 221
Final Meeting: Tuesday, May 8, 12:00 Noon
Instructor: Doug Baldwin
Office: South 307
Phone: 245-5659
Email: baldwin@geneseo.edu
Office Hours: Any time Monday through Friday, 8:00 AM to 5:00 PM, when I’m not committed
to something else. See my
Calendar for details and to make appointments electronically. You don’t need to make
appointments to see me, but may if you want to be sure I’ll be available.
Outline of Course Materials: http://www.geneseo.edu/~baldwin/math223/spring2018/course.php
Until now, your “official” education in math (you may, of course, have learned more than you were “officially” taught) has used a very straightforward notion of what a function is: a function has one argument, and computes one result from that argument. Calculus III considers what happens when we broaden that view to include functions that have more than one argument, or that produce more than one result, or both. In particular, we will consider what it means for such a function to have a limit, how you might differentiate or integrate such a function, etc.
We will also look at some of the real-world uses of multivariable and vector-valued functions (those are the technical names for functions with multiple arguments and multiple results, respectively). There are lots of applications, because most of the real world needs multiple values to describe it — atmospheric scientists think of air temperature as a function of latitude, longitude, and altitude (and time); physicists compute forces in terms of both how strong they are and what direction they push in; the list of examples goes on through many other natural and social sciences. My own interests are particularly caught by applications of this material to computer graphics — any time you see a 3-dimensional surface in a computer game or animation, you are probably looking at a multivariable and/or vector-valued function.
Prerequisite(s): Math 222
Learning Outcomes: On completing this course, students who meet expectations will be able to…
The (required) textbook for this course is
Openstax, Calculus Volume 3
This is a free electronic text available at
https://openstax.org/details/books/calculus-volume-3
One of this course’s goals is to develop your awareness of technological tools for graphing and otherwise working with multivariable and vector-valued functions. The tool we will use is “muPad,” the computer algebra system in Matlab. You will therefore need a copy of Matlab (version r2017a) installed on your computer. You can get copies for either Macintosh or PC computers from Geneseo, at
http://software.geneseo.edu
(Scroll down through the list of software until you find Matlab)
Instructions for installing Geneseo’s Matlab on your own computer are at
https://wiki.geneseo.edu/display/cit/MatLab+Installation+Guide
The copy of Matlab you get from Geneseo will only run on a computer connected to the Geneseo network. If you commonly work off campus, you can use a “virtual private network” (VPN) to make it look like your computer is on Geneseo’s network. The VPN is simply a piece of software you install on your computer. Windows users can download the “Cisco VPN” package from software.geneseo.edu. Macintoshes come with a VPN pre-installed; follow the instructions at https://wiki.geneseo.edu/display/cit/Setting+up+Geneseo+VPN+on+macOS to activate it.
Materials from the last time I taught this course are available through
https://www.geneseo.edu/~baldwin/math223/spring2016/syllabus.php
The following dates are best estimates. They may well change as students’ actual needs become apparent. Refer to the Web version of this syllabus for the most current information, I will keep it as up-to-date as possible:
| Jan. 17 - Jan. 18 | Introduction |
| Jan. 18 - Jan. 24 | 3D Analytical Geometry |
| Jan. 24 - Feb. 2 | Vectors and their Use in 3D Geometry |
| Feb. 2 - Feb. 26 | Vector-Valued Functions |
| Feb. 26 | Hour Exam 1 |
| Feb. 26 - Mar. 1 | Introduction to Multivariable Functions |
| Mar. 1 - Mar. 29 | Derivatives of Multivariable Functions and some Applications |
| Mar. 29 | Hour Exam 2 |
| Mar. 29 - Apr. 11 | Integrals of Multivariable Functions and some Applications |
| Apr. 11 - Apr. 30 | Vector Calculus |
| May 8 | Final Exam |
Your grade for this course will be calculated from your grades on exercises, exams, etc. as follows:
| Final | 30% |
| Hour Exams (2) | 20% each |
| Problem Sets (8 - 10) | 25% |
| Participation | 5% |
In determining numeric grades for individual assignments, questions, etc., I start with the idea that meeting my expectations for a solution is worth 80% of the grade. I award the other 20% for exceeding my expectations in various ways (e.g., having an unusually elegant or insightful solution, or expressing it particularly clearly, or doing unrequested out-of-class research to develop it, etc.); I usually award 10 percentage points for almost anything that somehow exceeds expectations, and the last 10 for having a solution that is truly perfect. I deliberately make the last 10 percentage points extremely hard to get, on the grounds that in any course there will be some students who routinely earn 90% on everything, and I want even them to have something to strive for. I grade work that falls below my expectations as either meeting about half of them, three quarters, one quarter, or none, and assign numeric grades accordingly: 60% for work that meets three quarters of my expectations, 40% for work that meets half of my expectations, etc. This relatively coarse grading scheme is fairer, more consistent, and easier to implement than one that tries to make finer distinctions.
This grading scheme produces numeric grades noticeably lower than traditional grading does. I take this into account when I convert numeric grades to letter grades. The general guideline I use for letter grades is that meeting my expectations throughout a course earns a B or B+. Noticeably exceeding my expectations earns some sort of A (i.e., A- or A), meeting most but clearly not all some sort of C, trying but failing to meet most expectations some sort of D, and apparently not even trying earns an E. I set the exact numeric cut-offs for letter grades at the end of the course, when I have an overall sense of how realistic my expectations were for a class as a whole. This syllabus thus cannot tell you exactly what percentage grade will count as an A, a B, etc. However, in my past courses the B+ to A- cutoff has typically fallen somewhere in the mid to upper 80s, the C+ to B- cutoff somewhere around 60, and the D to C- cutoff in the mid-40s to mid-50s. I will be delighted to talk with you at any time during the semester about your individual grades and give you my estimate of how they will eventually translate into a letter grade.
I am offering a “real-world math bounty,” i.e., an invitation to find problems in other classes, current events, your own daily life, etc. that could be discussed in class and solved using the math we are learning. For each such problem you bring to me and that we can potentially use in class, I will give you 1 point of extra credit, up to a maximum of 10. You should describe each problem in your own words, and please don’t bring homework assignments from another class to do as examples in this one, but apart from those rules I want this to be a flexible and fun way to bring examples into the course.
Mathematical notation and terminology matter. Even though they may seem arcane, each symbol and technical term has a specific meaning, and misusing symbols or terms (including not using them when you should) confuses people reading or listening to your work. Therefore, correct use of mathematical terms and notations will be a factor (albeit probably a small one) in grading assignments and tests in this course.
(The same applies to me, by the way: if you think I’m not using terms or notations correctly, or you just aren’t sure why I’m using them the way I do, please question me on it.)
Calculators, computer algebra systems, and similar automatic tools for doing math may not be used on homework exercises except where explicitly permitted; on the other hand, they may be used freely on exams.
(Since this may seem like a strange, or even backwards, rule, here is the reason for it. As mathematicians — and yes, anyone taking calculus 3 is at least partly a mathematician — you face a dilemma concerning calculators. On the one hand, no-one in the “real world” does math by hand that a machine can do instead; on the other hand doing math by hand does, over time, build intuition for how and why it works the way it does. So I think you should both learn to use calculators, and at the same time practice doing without them. Of all the places you will “do math” in this course, exams are the place where the real-world merit of calculators, namely being time-saving devices that free people up to focus on the creative parts of a problem, most pays off. Conversely, the place where you most have time to reflect on manual mathematics, and where it is easiest for me to check or assist with it, is the homework exercises.)
I will accept exercise solutions that are turned in late, but with a 10% per day compound late penalty. For example, homework turned in 1 day late gets 10% taken off its grade; homework turned in 2 days late gets 10% taken off for the first day, then 10% of what’s left gets taken off for the second day. Similarly for 3 days, 4 days, and so forth. I round grades to the nearest whole number, so it is possible for something to be so late that its grade rounds to 0.
I do not normally give make-up exams.
I may allow make-up exams or extensions on exercises if (1) the make-up or extension is necessitated by circumstances truly beyond your control, and (2) you ask for it as early as possible. At my discretion, I may require proof of the “circumstances beyond your control” before granting a make-up exam or extension.
Assignments in this course are learning exercises, not tests of what you know. You are therefore welcome to work on them in small groups, unless specifically told otherwise in the assignment handout—a well-managed group makes a successful, and thus more educational, project more likely.
In order to avoid confusion when people work together, please indicate clearly what work is yours and what comes from other sources on everything you hand in. The appropriate “indication” depends on how much work is yours and how distinguishable it is from your collaborators’. At one extreme, if a group of people work together on all parts of an assignment, they could hand in one solution with all their names, and a brief statement of what each person contributed, on it. At the other extreme, if you do most of an assignment on your own but get a specific idea from someone else, you might just include a comment or footnote to the effect of “this idea comes from Betty Smith” in whatever you hand in. The bottom line is that everything you take credit for must include some identifiable contribution by you, and you should never claim credit for work or ideas that aren’t yours. I’ll be glad to advise you on what I consider appropriate forms and acknowledgements of collaboration in specific cases if you wish.
Please note that tests are tests of what you know, and working together on them is explicitly forbidden. This means that if you take advantage of the collaboration policy to avoid doing your share of the work on the exercises, you will probably discover too late that you haven’t learned enough to do very well on the tests.
I will penalize violations of this policy. The severity of the penalty will depend on the severity of the violation.
SUNY Geneseo will make reasonable accommodations for persons with documented physical, emotional, or cognitive disabilities. Accommodations will be made for medical conditions related to pregnancy or parenting. Students should contact Dean Buggie-Hunt in the Office of Disability Services (tbuggieh@geneseo.edu or 585-245-5112) and their faculty to discuss needed accommodations as early as possible in the semester.