Syllabus for Partial Differential Equations

Professor: Mark McClure

Course purpose

As you learn in Math 394, differential equations are the mathematical tool used to model quantities that change continuously over time. We use PDEs to model quantities which vary over time and space - kinda like the Twilight Zone! In this class, we'll learn about

• Modeling: A mathematical abstraction of physical reality is called a model. We'll discuss models of heat flow, vibration, and other complicated phenomena.
• Analytics: What is a solution to a partial differential equation? How can we find one satisfying certain boundary and/or initial conditions? The techniques for PDEs are surprisingly different than those for ODEs.
• Numerics: Suppose we can't find a solution. How can we approximate a solution?
• Qualitative analysis: What type of simple, qualitative thinking provides a check on our symbolic and numerical analysis?

Materials

• Text: We will use the third edition of Applied Partial 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
  • PDE Talk: Our online forum
• Technology: This class will have a significant online component, even if you attend in person. 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.
  • PDE Talk: I've set up an online forum called PDE Talk where we can discuss all aspects of PDEs. Not only is this a great place ask questions but participation is mandatory. You will earn points for certain assigned questions.
  • Computational tools: I've developed some web-based tools to ease the process of computing with PDEs. We might use Mathematica or Python later in the semester.

Course structure

This course is offered in the "hybrid" mode, which gives us a lot of flexibility to deal with the unique challenges the last year has brought. My intention is to provide as much flexibility to students as possible. To that end:

• I will generally teach in the classroom. All students have the option to come to the room or attend via Zoom.
• On occasion, I might choose to teach remotely; thus, all students need to be prepared to Zoom in, when that happens.
• I don't intend to record the classes, though it's fine with me if students do record the classes.
• All assessment will be done remotely, as described below.

Grades

There will be three major components to your grade, all of which can be done remotely:

• Semi-frequent forum posts
• Two major typed assignments. I expect these to be due
  • the week of February 15 and
  • the week of April 5.
• Two hour and a half long exams. These will probably be on
  • Monday, March 8 and
  • Monday, April 26.

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.