SUNY Geneseo Department of Mathematics
Spring 2023
Prof. Doug Baldwin (he/him/his)
Last modified June 1, 2023
Time and Place: MTWF 12:30 - 1:20 PM, Bailey 102
Final Meeting: Monday, May 15, 12:00 - 3:20 PM
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 Google
Calendar for details of when I’m free and to make appointments
electronically. You don’t need to make appointments to see me, but I recommend
it in order to be sure I’ll be available. I find that office hours are most
effective when they’re in-person in my office, but if you need to, I’ll be
happy to meet in other ways or places. Finally, office hours don’t need to be
just about this course — feel free to come see me any time you have something
you’d like to talk about.
Online Course Materials: https://www.geneseo.edu/~baldwin/math223/spring2023/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 produces 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, you should be able to…
This course is designated as “face-to-face.” That means that class meetings will be in person as much as possible, although it doesn’t rule out occasional online activities.
For each topic we study, I will follow a pattern that begins with you reading (or maybe watching a video, etc.) about the basic ideas of that topic, then talking about and working with it in class. After each class meeting, I will produce a summary of the key ideas, questions, and answers from it, and post the summary online. Each week I will also ask you to work with ideas more on your own via a homework exercise. I will meet with you outside of class to discuss each of these exercises and to share my feedback. Each of these aspects of the course, i.e., readings, in-class activities, notes, homework, and meetings, contributes to your learning; you will get the most out of the course if you do all of them. However, there is also a certain overlap between the different parts of the course, so that if you can’t do one, especially if it’s only for a limited time, you can make up for it by concentrating more on the others. So if, for example, you have to miss some class meetings for illness or family emergencies, don’t panic! You will still be able to participate and succeed in the course through the other channels. Naturally, not engaging with enough of the course will eventually lead to an unrecoverable situation, but the course format deliberately accomodates occasional situations in which you can’t do everything.
The (required) textbook for this course is
LibreTexts, Math 223 Calculus 3
This is a free online text adapted from other open educational resources for this course. You can read it online at
https://math.libretexts.org/Courses/SUNY_Geneseo/Math_223_Calculus_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. We will use Mathematica, a popular symbolic math system. You will need a copy of Mathematica installed on your computer. Follow the instructions for doing this at
https://wiki.geneseo.edu/display/cit/Mathematica+Installation+and+Licensing+Instructions
Materials from the last time I taught this course are available at
https://www.geneseo.edu/~baldwin/math223/fall2022/course.php
Note that the following dates are best estimates. They may change as our 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. 24 - 25 | Introduction |
| Jan. 25 - Feb. 3 | 3D Analytic Geometry |
| Feb. 3 - Feb. 15 | Vectors and their Use in 3D Geometry |
| Feb. 15 - Mar. 1 | Vector-Valued Functions |
| Mar. 1 - Apr. 5 | Multivariable Functions and their Derivatives |
| (Mar. 11 - Mar. 19 | Spring Break) |
| Apr. 5 - Apr. 19 | Integrals of Multivariable Functions |
| Apr. 19 - May 10 | Vector Calculus |
Grading in this course will be very different from what you are used to. The main reason for the unusual grading is that I am trying to consciously undo some of the small ways in which conventional grading unconsciously disadvantages certain students. But beyond removing disadvantages for some, I believe that what I am doing also offers significant advantages to everyone.
There are 3 main ways in which grading in this course will probably differ from what you have seen before.
“Achieving” an outcome has two components: content, i.e., what ideas you know, and depth of understanding, i.e., how thoroughly you understand those ideas. This course’s learning outcomes define both components. Generally speaking, the nouns in the outcomes correspond to content, i.e., things you will learn about. Verbs in the outcomes indicate depth of understanding, i.e., things you will understand the content well enough to do.
I will give you a numeric grade for each outcome in an exercise, based mainly on the discussion of solutions and similar problems — in other words, getting the right answers matters, but is not the only, or even the main, determiner of your grade. Grades range from 0 to 4, as follows:
| 4 | Mastery as required by the learning outcome throughout the exercise |
| 3 | Approaching the required mastery; you can explain how to solve most problems arising from the exercise, but make mistakes in the details of doing it |
| 2 | Partial mastery; you can correctly solve most problems but not explain how you solved them |
| OR you can explain how to solve most problems, but not put those ideas into practice | |
| OR you can explain and correctly solve some but not most of the problems | |
| 1 | Initial steps towards mastery; you can begin doing the exercise but not carry solutions to completion or explain how you would do so |
| 0 | No understanding of this outcome yet |
Although I will grade each exercise, mastery grading isn’t about how you do on any specific one. It’s about how well you’ve achieved outcomes by the end of the course. To that end, there are two other important points about exercises and their grades:
You will “turn in” each exercise by sharing your solution with me during one of your individual meetings. During that meeting, we’ll go over your solutions and answer any questions you have about them, and we’ll also discuss how you came up with those solutions and how you would approach similar problems.
Finally, when this course ends I will give you a letter grade for it based on the numeric grades. My approach to this is that B grades (including B- and B+) indicate that you generally met the expectations of the course, A grades that you distinctly exceeded them, and grades below B- that you fell short to varying degrees. However, I won’t decide the exact cut-offs between grades until the end of the semester, when I see how grades actually worked in practice. During the semester, you can use the mastery rubric as a qualitative guideline to how you’re doing — for example, it says that 3 out of 4 points, or 75%, is “approaching the required mastery,” so an overall average of 75% should indicate that you’re doing OK but maybe not quite as well as desired. I will be happy to discuss your grades with you at any time during the semester and give you my sense of what letter grade, or range of letter grades, I think you are heading for.
Assignments in this course are fundamentally learning exercises. You are therefore welcome to help each other with them, unless specifically told otherwise in the assignment handout. However, solutions that you turn in must represent your own understanding of the solution and must be written in your own words, even if you got or gave help on the assignment.
If you use sources other than this class’s textbook or notes in order to do an assignment, you must include a comment or footnote citing those sources in your solution. Similarly, if you get help from anyone other than me you must acknowledge the helper(s) somewhere in your solution. (But note that I generally think learning from outside sources and people is a good thing, not a bad one.)
I will penalize violations of this policy. The severity of the penalty will depend on the severity of the violation.
To foster a more inclusive, diverse, and safe space in this class, you have a right to express who you are in the classroom, in meetings, etc. This includes, but isn’t limited to, the right to speak, write, and think in the language forms or dialects you grew up with or identify in, the right to share your prefered name and/or pronouns if you wish and have others use them, etc.
Rights come with responsibilities, however. In this case, you have a responsibility to exercise your right to express yourself only in ways that don’t limit others’ right to expression, nor their right to learn in a safe and welcoming environment.
Students’ right to their own language notwithstanding, 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 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.)
Mathematica, calculators, and similar automatic tools for doing math may not be used on homework exercises except where explicitly permitted.
(Since this may seem like a strange rule, here is the reason for it: as math students 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, and one of the goals of this course is even to introduce you to a “machine” tool for math; 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 — or, for this course, Mathematica — and at the same time practice doing without them. So some homework exercises will explicitly let you practice with Mathematica, but those that don’t are deliberately places to practice doing without its help.)
The college provides a range of support services to help students thrive in their classes. Of these services, the one best suited to this course is the Math Learning Center. For more information, including hours and procedures for scheduling a visit, see the MLC website at https://www.geneseo.edu/math/mlc.
Other on-campus tutoring services include the Writing Learning Center (https://www.geneseo.edu/english/writing_center) and a range of department-based tutoring centers.
The SUNY-wide STAR-NY system (www.starny.org/tutoring_schedule) provides online tutoring in a wide variety of subjects.
For more information on these and other academic support services, see the Academic Support Services website at https://www.geneseo.edu/academic-support-services.
SUNY Geneseo is dedicated to providing an equitable and inclusive educational experience for all students.
The Office of Accessibility will coordinate reasonable accommodations for persons with physical, emotional, or cognitive disabilities to ensure equal access to academic programs, activities, and services at Geneseo. Students with letters of accommodation should submit a letter to each faculty member and discuss their needs at the beginning of each semester. Please contact the Office of Accessibility Services for questions related to access and accommodations.
Office of Accessibility Services
Erwin Hall 22
(585) 245-5112
access@geneseo.edu
https://www.geneseo.edu/accessibility-office
Under state law (Education Law, Section 224-a) students are excused from course requirements, such as examinations, class attendance, or other academic study and work requirements, for religious observance. You can make up any work missed in such circumstances without penalty. Geneseo’s complete policy on religious observances, with links to common holidays, is available at https://www.geneseo.edu/apca/classroom-policies.
Individuals on active military duty (including National Guard and Reserve service) are entitled to excused absences from classes during their period of service and will not be penalized in any way. See the College Bulletin for more on this policy.
If there is anything else I can do to make this class or its materials easier for you to access or use, please let me know.
Geneseo offers many other services to help students succeed. For a list of some, see https://wiki.geneseo.edu/display/PROVOST/Syllabus+Resources+Related+to+Student+Success.