University of Illinois at Urbana-Champaign

Math 385 (Differential Equations and Orthogonal Functions) Spring 2007

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).


Current course grades : click on `Score Reports'

Homework assignment for the current week

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. 15 1.1: Differential Equations and Mathematical Models
1.2: General and Particular Solutions
no class on Mon, 1/15 MLK, Jr. Day
Jan. 22 1.4: Separable Equations
1.5: Linear First-Order Equations
1.3: Slope Fields
first IODE lab
Jan. 29 1.6: Substitution Methods and Exact Equations
2.1: Population Models
Feb. 5 2.2: Equilibrium Solutions
2.4: Euler's Method
2.5: Improved Euler's Method
second IODE lab, first IODE project due
Feb. 12 3.1: Second-Order Linear Equations
3.3: Homogeneous Equations with Constant Coefficients
Feb. 19
3.2: General Solutions of Linear Equations First midterm exam covering chapters 1 and 2
Feb. 26 3.4: Mechanical Vibrations
3.5: Nonhomogeneous Equations
second IODE project due
Mar. 5 3.5
3.6: Forced Oscillations and Resonance
Mar. 12 3.8: Boundary Value Problems and Eigenvalues third IODE project due
Mar. 26 9.1: Periodic Functions and Trigonometric Series
9.2: General Fourier Series
Second midterm exam covering chapter 3
Apr. 2 9.3: Fourier sine and cosine series
9.4: Applications of Fourier series
Apr. 9 9.5: Heat Conduction and Separation of Variables
9.6: Vibrating Strings and the Wave Equation
fourth IODE project due
Apr. 16 9.6
9.7: Steady-state temperature and the Laplace equation
Apr. 23 8.2: Power Series Solutions near ordinary points
8.3: Power Series Solutions near regular singular points
fifth IODE project due
Apr. 30 - review for final exam, sixth IODE project (extra credit) due