Math 285. Differential Equations
Iode version Syllabus for Instructors

Text: Edwards and Penney, Differential Equations with Boundary Value Problems: Computing and Modelling, Custom Edition for the University of Illinois at Urbana-Champaign, Pearson Custom Publishing, 2008.

Note: This custom edition is taken from Edwards and Penney, Differential Equations with Boundary Value Problems: Computing and Modelling, Fourth Edition. It is identical to the fourth edition except that Chapters 5, 6, 7, and 8 have been removed. If students would prefer to use the full fourth edition, this should not be a problem. The full fourth edition is the standard text for Math 286.

About Iode

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.

• 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)

• Section 2.2: Equilibrium Solutions and Stability [parts of Section 2.1 could be incorporated here also] (1 hour)
• Sections 2.4 and 2.5, and Iode Lab 2: Euler's method and refinements (3 hours)

Chapter 3 - Linear Equations of Higher Order (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: Endpoint problems (2 hours)

Chapter 9 - Fourier Series Methods (13 hours)

• Sections 9.1 and 9.2: Fourier series (3 hours)
• Iode Lab 4: Convergence of fourier series (1 hour)
• Section 9.3: Fourier sine and cosine series, termwise differentiation (2 hours)
• Section 9.4: Applications of Fourier series (1 hour)
• Section 9.5: Heat conduction and separation of variables (2 hours)
• Section 9.6: Vibrating strings and the wave equation via separation of variables (2 hours)
• Section 9.7: Steady-state temperature and Laplace's equation via separation of variables - emphasize the semi-infinite strip and the disk (2 hours)

Examinations, review, and leeway (5 hours)

Total: 43 hours

Notes:
In Section 2.2, Laugesen strongly recommends drawing all phase lines vertically rather than horizontally. That is, if you have a DE of the form dy/dx=f(y) then draw the phase line vertically as the y-axis. [This allows students to easily sketch solution curves in combination with the phase line, a task they otherwise find very difficult when using horizontal phase lines as drawn in the textbook.]

Using Iode in Your Class

This syllabus devotes one hour to each of 4 Iode Labs, although experience has shown that only the first 2 Labs really *require* class time. It is possible to cover the later 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 during the first third of the semester. This forces 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. Note 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. Instructors should also 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 have only about 35 terminals. Instructors with larger classes can reserve two adjacent labs in Engineering Hall, or else can reserve one lab hour during the normal class period and another one in late afternoon (for example)."

Assessment