Section 1 Introduction to Math 2575
Welcome to Math 2575, Accelerated Calculus III. I’m happy to have you here with me as we complete the final semester of calculus. In my opinion, the last chapters in the calculus sequence are the most interesting, so you’re in for a treat!
There are many of us in this class, coming from many different backgrounds and situations. I want my classroom to be as inclusive as possible. If the “default settings” for the class don’t work for you, please don’t hesitate to ask for accommodation. Some accommodations will be universally available, in recognition of the fact that the pandemic is not, in fact, over.
We begin with some introductions: to the university, to the staff, and to the course.
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.)
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moodle.uleth.caDon’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.
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www.uleth.ca/services-for-students/health-safetySubsection 1.2 Course staff and contact information
My name is Sean Fitzpatrick. I can be reached via email at sean.fitzpatrick@uleth.ca.
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www.cs.uleth.ca/~fitzpat4
mailto:sean.fitzpatrick@uleth.ca
Office 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.
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.
