Syllabus for Differential Equations

Professor: Mark McClure

Course purpose

Three semesters of calculus really culminate in Differential Equations which forms the ultimate language of dynamics and change. Newton's motivating application of calculus (an understanding of the motions of the heavens) boiled down to describing that motion with a set of differential equations and then trying to understand those equations. In this course we will study:

• Modeling: Differential equations are the mathematical tool used to model quantities that vary continuously with time.
• Analytics: What is a solution to a differential equation? How can we find one? What does it tell us?
• Qualitative analysis: Suppose we can't find a solution. What information can we obtain from the geometry of the equation?
• Numerics: Taking qualitative analysis a bit further, how can we find precise, though not exact, information from an unsolvable equation?

Materials

• Text: We will use the third edition of A First Course in Differential Equations by J. David Logan. Through a special arrangement between The University and the publisher, you can download a PDF or ebook through the library link below. You are not required to purchase this text, though you may obtain an hard copy from Amazon, if you choose.
  • Library Access (UNCA Login required) and/or
  • Purchase from Amazon
• Websites
  • MyOpenMath: Our auto graded homework system
  • ODE Talk: Our online forum
• Technology: This class will have a significant online component. As such, a decent computer and reliable internet connection are essential. All required software is either open source, available via a UNCA site license, or will be accessed via the web - including:
  • Zoom: For attending class remotely.
  • MyOpenMath: We will have some auto-graded homework using MyOpenMath. You can login there, using the information presented in class.
  • Stat Talk: I've set up an online forum called Stat Talk where we can discuss all aspects of statistics. Not only is this a great place ask HW questions but participation is mandatory. You will earn points for certain assigned questions.
  • Python/Anaconda: An open source language and environment for scientific computing and graphics. This is the tool that will allow us to work with large, real world data sets. You can download a copy from here. Anaconda is also installed in the math lab.

Course structure

This course is offered as a "hybrid" course, meaning that it will run partly in person and partly online. According to the "official" schedule, we're supposed to meet M in the classroom and W online. I'd prefer to offer as much flexibility as possible, however. With that in mind, all classes will be available via zoom. I might come in on Wednesdays to deliver lecture as well, if the room is available.

Having said that, you are expected to attend class and participate; it will affect your grade, as described below.

Grades

All assessment will be done remotely; there will be no in class quizzes or exams.

• Homework: There will be two types of graded homework:
  • MyOpenMath, which is online and automatically graded.
  • Forum posts.
• Quizzes: We'll have a few quizzes, which will essentially be short but timed MyOpenMath sessions.
• Computer Labs: A major part of the class will involving using the computer to work with large data sets. Thus, we'll have several computer labs to help with this.
• Participation: You will earn up to 60 points simply for attending regularly (in-person or online), asking questions, and participating in any in class labs or problem sessions.
• Final grades: I will determine final grades using a scale not more stringent than the standard 90-80-70-60 scale. You will be apprised of your standing as the term progresses.
• Late work: In general, I don't accept late work.

Advice

• Help: You are not undertaking this challenging task alone. Here are a few sources of assistance:
  • Me: I like to talk to people about math and stat! That's why I chose this profession. You can find me on Zoom most days between 9:30 and 10:30, as well as on our forum.
  • Your classmates: Most people learn best by talking things through with others. You will find that you can both learn from and help your fellow classmates. In particular, if your classmate is explaining a fine point to you, then you are helping them!
  • Our class forum: A kinda combination of the previous two that never sleeps!
  • The Math Lab: The Math Lab has always rocked! It's now available for both in person and online tutoring, as detailed on their webpage.

Your rights and responsibilities

It's worth understanding your rights and responsibilities as a student at UNCA. One of my responsibilities is to make sure you have the information that you need to do that. Since this is common to all classes, I've got that information on this legalese document.