University of Illinois at Urbana-Champaign

Math 285 (Differential Equations and Orthogonal Functions) Spring 2004

Course Description

This course is an introduction to differential equations, with particular emphasis on boundary value problems and series solutions. Topics we will cover include homogeneous and nonhomogeneous linear equations, boundary value and eigenvalue problems, and Fourier series methods. Numerical and graphical methods will play an important role throughout the semester. We will be using an interactive differential equations program called IODE developed here at the University of Illinois. Some of the class meetings will occur in one of the Engineering workstation (EWS) labs and some of the homework projects will require you to use this system.

The prerequisite for this course is completion of one of the multivariable calculus courses (Math 242, 243 or 245).


Homework assignment for the current week

Solutions to past homework, quizzes, etc.

Course announcements

Lecture Log


Schedule of Topics

(Note: This schedule is tentative and may be revised at a later date.)

Week of Topics Remarks
Jan. 19 1.1: Differential Equations and Mathematical Models
1.2: General and Particular Solutions
1.4: Separable Equations
no class on Mon, 1/19 MLK, Jr. Day
Jan. 26 1.3: Slope Fields
1.5: Linear First-Order Equations
first IODE lab
Feb. 2 1.6: Substitution Methods and Exact Equations
2.1: Population Models
2.2: Equilibrium Solutions
Feb. 9 2.4: Euler's Method
2.5: Improved Euler's Method
second IODE lab, first IODE project due
Feb. 16 3.1: Second-Order Linear Equations
3.3: Homogeneous Equations with Constant Coefficients
second IODE project due
Feb. 23
3.2: General Solutions of Linear Equations First midterm exam on 2/27 covering chapters 1 and 2 (sections 2.1, 2.2, 2.4, 2.5 only)
Mar. 1 3.4: Mechanical Vibrations
3.5: Nonhomogeneous Equations
Mar. 8 3.6: Forced Oscillations and Resonance
3.8: Boundary Value Problems and Eigenvalues
Mar. 15 9.1: Periodic Functions and Trigonometric Series
9.2: General Fourier Series
Mar. 29 9.2 third IODE project (cancelled)
Second midterm exam on 4/2 covering chapter 3 (sections 3.1-3.6 and 3.8 only)
Apr. 5 9.3: Fourier sine and cosine series
9.4: Applications of Fourier series
Apr. 12 9.5: Heat Conduction and Separation of Variables fourth IODE project due
Apr. 19 9.6: Vibrating Strings and the Wave Equation fifth IODE project due
Apr. 26 9.7: Steady-state temperature and the Laplace equation -
May 3 - review for final exam, sixth IODE project (extra credit)

Final Exam on 5/14 from 8:00 to 11:00 am in 100 Gregory Hall (note change of room!)