Math 385 Iode version syllabus

About Iode

Iode is a software package developed in this department by Peter Brinkmann, Richard Laugesen, and Robert Jerrard for use in Math 385 and similar classes. It can be installed and learned in minutes. Information and basic orientation on Iode is available from Richard Laugesen.

Iode sections of Math 385 mostly follow a traditional lecture format, but the class also meets a few times over the course of the semester in computer labs, and some homework assignments involve work with Iode. The syllabus is correspondingly slightly different from the traditional syllabus.

chapter 1 - first-order ODEs: 7 hours

• Sections 1.1 through 1.3 (3 hours)
• Iode Lab 1: introduction to Iode, and slope fields (1 hour)
• Sections 1.4 through 1.6 (3 hours)

chapter 2 - more on first-order ODEs: 4 hours

• Sections 2.4 and 2.5, and Iode Lab 2: Euler's method and refinements (3 hours)
• Section 2.2: equilibrium solutions and stability (1 hour)

chapter 3 - higher order linear equations: 14 hours

• Sections 3.1 and 3.2: general material on existence and uniqueness of solutions of linear equations. (3 hours)
• Section 3.3: homogeneous constant coefficient equations (2 hours)
• Iode Lab 3: second order equations (1 hour)
• Section 3.4: mechanical vibrations (2 hours)
• Section 3.5: nonhomogeneous equations (2.5 hours)
• Section 3.6: forced oscillations and resonance (1.5 hours)
• Section 3.8: eigenvalue problems (2 hours)

chapter 9 - Fourier series and separation of variables: 13 hours

• Sections 9.1 and 9.2: Fourier series (3 hours)
• Iode Lab 4: convergence of fourier series (1 hour)
• Section 9.3: Even and odd Fourier series, termwise differentiation (2 hours)
• Section 9.4: Fourier series and ODEs (1 hour)
• Section 9.5: the heat equation and separation of variables (2 hours)
• Section 9.6: the wave equation via separation of variables (2 hours)
• Section 9.7: Laplace's equation via separation of variables - emphasize the semi-infinite strip and the disk (2 hours)

Examinations, review, and leeway

total

About Iode Labs

The developers of Iode have written a number of Iode Labs and Projects. These are available on the Iode web page, along with solutions for the Projects. Projects are intended as homework assignments and Labs as in-class exercises, but instructors are welcome to use the material as they see fit, and also to suggest modifications or additions to the existing archive of Iode-related materials.

This syllabus devotes one hour to each of 4 Iode Labs. Iode Projects are designed to accompany the Iode Labs and can be assigned as homework soon after the lab sessions.

For Iode Labs it is necessary to reserve lab space in advance in the Engineering Work Stations (EWS) labs. This is done very easily using an online system; for more information ask Richard Laugesen. Some instructors may also want to reserve lab space for office hours when assigning Iode Projects. TAs can be asked to help out with lab office hours.

The computer labs we use only have about 35 terminals. Instructors with larger classes can handle this by reserving an two hours of lab space for every one-hour Iode Lab, one during the normal class period and one in late afternoon (for example), and letting students attend either session. Sections of Math 385 rarely have much more than 70 students, and so this should be adequate.

It is also possible to cover some of the Iode material by a combination of standard classroom lectures and abundant office hours in the lab. However, we strongly recommend that every Iode section meet in the lab for the first two Iode Labs, which both occur in the first third of the semester. This forces the students to get acquainted with the software and drives home the point that Iode is an essential part of the course. We also strongly recommend that Iode Projects 1 and 2 be assigned as homework.