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## Math 285 Iode version syllabus

Iode is a software package developed at the University of Illinois, Urbana-Champaign, by Peter Brinkmann, Richard Laugesen and Robert Jerrard, for use in undergraduate differential equations courses. The software can be installed and learned in minutes. Information and basic orientation on Iode is available from Richard Laugesen.

Iode sections of Math 285 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)

5 hours.

43 hours.

### About Iode Labs

The developers of Iode have written a number of Iode Labs and Projects. These are available at the Iode web site, 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 these Labs, and can be assigned as homework soon after the lab sessions.

For the Iode Labs it is necessary to reserve lab space in advance at the Engineering Work Stations (EWS) labs. This is done by an online booking 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 only have 35-40 terminals. Instructors with larger classes can reserve two nearby labs at the same time.

We strongly recommend that every Iode section meet in the lab for the first two Iode Labs, which occur in the first third of the semester. This forces the students to get acquainted with the software. The later Labs can be covered by the students themselves, in preparation for the following Project.

To emphasize that Iode is an essential part of the course, the tests and final exam should include questions about the Project material.

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