Math 2575 Course Outline

Subsection 1.1 Welcome to the University of Lethbridge

Oki, and welcome to the University of Lethbridge. Our University’s Blackfoot name is Iniskim, meaning Sacred Buffalo Stone. The University of Lethbridge acknowledges and deeply appreciates the Siksikaitsitapii peoples’ connection to their traditional territory. We, as people living and benefiting from Blackfoot Confederacy traditional territory, honour the traditions of people who have cared for this land since time immemorial. We recognize the diverse population of Aboriginal peoples who attend the University of Lethbridge and the contributions these Aboriginal peoples have made in shaping and strengthening the University community in the past, present, and in the future.

As usual, everything you need to know for the course will flow through our Moodle learning management system. Make sure you check in regularly to keep on top of what's happening in the course. (Possibly the hardest part of learning online is keeping track of deadlines.)

Don't hesitate to reach out if you have questions. I'll do my best to answer all of your course-related questions as quickly as possible. (See Section 3 for details on how to get in touch.) If you have questions that are not related to the course, you can ask those too, and I'll try to answer, or to direct you to someone who can. Some resources can be found on the University's Health and Safety website.

Subsection 1.2 Course staff and contact information

My name is Sean Fitzpatrick. I can be reached via email at sean.fitzpatrick@uleth.ca.

Student hours: you are not going to get everything you need during class time. I will be available throughout the week for consultation, either one-on-one, or in small groups. Monday through Thursday, you can book appointments using Calendly. You'll find the links for booking appointments on Moodle. Any appointment can be in person, or over Zoom — just indicate your preference when booking. Friday I will have drop-in student hours: 9:30 – 11:30 am in my office.

Subsection 1.3 Course description

Math 2575 deals with the calculus of vectors, and functions of several variables. We begin with vectors, and vector valued functions, before moving on to several variables, and then finally, combining the two at the end. Just like in one variable, differentiability corresponds to the existence of a linear approximation. We'll then explore multivariable versions of familiar topics, like critical points, extrema, and optimization.

Since Math 1410 is a prerequisite for this course, we can do a few things that don't always make it into a standard calculus course. (At many universities, linear algebra is taken after the calculus sequence is complete.) In particular, we'll be able to make better sense of the notion of linear approximation: the linear approximation to a surface is a plane; the linear approximation to a differentiable function is a matrix transformation!

We'll then move on to double and triple integrals, and finally, to vector calculus. Most of what we see in the standard curriculum for vector calculus was developed to deal with problems in Physics, and in particular, electrodynamics. Those of you who have done a course or two in Physics will hopefully be able to make some connections.

Subsection 1.4 Online instruction and COVID policies

This time, only one section is online, but we should be prepared to go remote at any time, either individually (if you have symptoms or have been exposed to COVID), or as a class (if the 4th wave continues to get out of control). Note that it is likely there will be times when a class has to be taught online because the instructor is unavailable. We are likewise not allowed to come to campus if unwell. I may also have to teach from home because one of my kids is sick and has to quarantine.

I will do my best to ensure that the course experience is as similar as possible for all students, including those enrolled in the online section.

Our COVID policies will be as follows:

• Masks are required for all in-person interactions, as per university policy. If you cannot wear a mask, I would be happy to have you join us in the online section. This rule is non-negotiable. If a student attending in person refuses to wear a mask, our options are to either cancel class, or remove the offending student from the classroom.

• If you are at all ill, you must stay home. I will make arrangements for any in-class work to be done remotely.

• If an instructor for an in-person lecture or tutorial has symptoms, but is well enough to teach, that class will be temporarily moved online. A Zoom link will be posted to Moodle should this occur.

• I have two children in elementary school who cannot yet be vaccinated. There is a good chance that at some point I will have to move a class online because I have to stay home with them. I will give you as much notice as possible if this happens, and do my best to minimize disruption.

Whether online or in person, you can expect:

• More emphasis on:

  • Conceptual understanding

  • Discussion

  • Context (the whole “what is this good for?” routine)

  • Being generally swell human beings

• Less emphasis on:

  • Memorization (because how am I gonna stop you from looking stuff up, anyway?)

  • Routine computational proficiency (let's be honest: the computer can do this better than us most of the time)

  • Tests and exams (so I can spend more time teaching and less time as the Math Police)

We are scheduled to meet in person as long as this is feasible. I hope you'll be able to make it to each class. There will be opportunities for discussion, and to work on problems (including ones you'll be handing in) with your classmates.

But our first priority this year is to protect the health of everyone. If you are feeling sick, please stay home. If you can, please let me know when you're unable to attend, so I can plan accordingly.

I'll do my best to also support asynchronous learning. Lots can be done on your own time, even if you do make it to class. The textbook is free, online, and full of videos. Most of our work is designed to be done as in-class exercises, but I can provide these to you online as needed.