University of Illinois at Urbana-Champaign

Math 285 (Differential Equations and Orthogonal Functions) Fall 2002

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).

Schedule of Topics

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

Week of Topics Remarks
Aug. 26 1.1: Differential Equations and Mathematical Models
1.2: General and Particular Solutions
Sept. 2 1.3: Slope Fields first IODE lab and project
Sept. 9 1.4: Separable Equations
1.5: Linear First-Order Equations
1.6: Substitution Methods and Exact Equations
Sept. 16 2.4: Euler's Method
2.5: Improved Euler's Method
2.6: Runge-Kutta Method
second IODE lab and project
Sept. 23 2.1: Population Models
2.2: Equilibrium Solutions
3.1: Second-Order Linear Equations
Sept. 30
3.2: General Solutions of Linear Equations
3.3: Homogeneous Equations with Constant Coefficients
First midterm exam on 10/1 covering all of chapter 1 plus 2.4, 2.5 and 2.6
Oct. 7 3.3
3.4: Mechanical Vibrations
third IODE project
Oct. 14 3.5: Nonhomogeneous Equations
3.6: Forced Oscillations and Resonance
Oct. 21 3.6
3.8: Boundary Value Problems and Eigenvalues
Chapter 3 Review
Oct. 28 9.1: Periodic Functions and Trigonometric Series Second midterm exam on 10/29 covering 2.1, 2.2 and 3.1-3.5
Nov. 4 9.2: General Fourier Series
9.3: Fourier sine and cosine series
Nov. 11 9.3
9.4: Applications of Fourier series
fourth IODE project
Nov. 18 9.4
9.5: Heat Conduction and Separation of Variables
fifth IODE project
Dec. 2 9.6: Vibrating Strings and the Wave Equation
9.7: Steady-state temperature and the Laplace equation
sixth IODE project (extra credit)
Dec. 9 9.7
10.1: Sturm-Liouville problems

Final Exam on 12/19 from 8:00 to 11:00 am