WeBWorK

Your first two WeBWorK sets have now been assigned and will be added to your Week 1 checklist shortly. Log in to start working on these sets. Both are due by Sunday, September 6 at 11:59pm:

  • 1-FirstOrderLinear
  • 2-SeparableEquations

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Linear first order equations

The Week 0 checklist includes instructions to read sections 1.1, 1.2, 1.3, and 2.1 of your textbook before our meeting on Tuesday. Section 2.1 covers linear first order differential equations. It’s important for you to know that your textbook approaches solving linear first order equations using a technique called variation of parameters. Other textbooks often use a technique called integrating factors. We’ll be sticking with variation of parameters for our class.

The author explains his reason for choosing variation of parameters in the preface. His point is that variation of parameters is a technique that comes up again and again when solving differential equations, so it’s good to see it for the first time in a relatively easy setting as early in the course as possible.

Actually, the full quote in the preface is kinda great; he’s basically saying, “Haters gonna hate!” very politely:

Traditionally oriented elementary differential equations texts are occasionally criticized as being collections of unrelated methods for solving miscellaneous problems. To some extent this is true; after all, no single method applies to all situations. Nevertheless, I believe that one idea can go a long way toward unifying some of the techniques for solving diverse problems: variation of parameters… You may find this annoying, since most of us learned that one should use integrating factors for this task, while perhaps mentioning the variation of parameters option in an exercise…. The advantage of using variation of parameters here is that it introduces the concept in its simplest form and focuses the student’s attention…

William F. Trench, Elementary differential equations

You are allowed to use the method of integrating factors instead of variation of parameters if you really want to, but if you do, your written work must be extremely clear. I have used the technique myself, but it’s been a very long time, so you shouldn’t assume I already know what you’re writing. It’s safer and better for later if you stick to variation of parameters.

The questions on the WeBWorK set 1-FirstOrderLinear offer you hints if you haven’t entered the correct answer after some number of tries. The hints assume that you’re using integrating factors, not variation of parameters, so they may not be very useful for you.

Course hub

I alluded to the lessons on the MAT 2680 course hub on our tour of our own course site in class on Thursday. These are session-by-session notes that my colleague, Professor Singh, put together for everyone to use.

Professor Singh’s notes on the course hub are new so I haven’t taken a close look at all of them yet. Some of the lessons follow our textbook pretty closely, but if you check out Lesson 1 on first order linear equations, you’ll see that he’s taken the integrating factors approach instead of variation of parameters.

I plan to stick pretty close to our textbook and assign you readings from it throughout the semester, but I’ll include links to the course hub where relevant.