Math 285 (Differential Equations and Orthogonal
Functions) Spring 2004
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.
Announcements of quizzes, tests, and general information related to the class can be found at https://math.uiuc.edu/~tyson/285/285s04announcements.html
Solutions copied directly from the back of the book or the IODE Solutions Manual will recieve no credit.
I will drop your lowest two homework scores when computing the final grade. (This does not include the IODE computer projects, which are mandatory.)
Non-Engineering students registered in this course must email me within the first week of classes with their NetID so that I can create an account for them in the EWS labs.
No late quizzes will be given, but if you miss a quiz for a reasonable and documented excuse as above, I will disregard that quiz when computing your final grade. At the end of the semester I will drop your lowest quiz grade.
No make-up exams will be given. If a midterm exam is missed because of a serious and documented illness or emergency, your semester grade will be determined on the basis of other work done in the course. Exams missed for other reasons will be counted as failures.
If you have a conflict with any of these dates, particularly with the date of the final exam, please contact me to discuss the matter as soon as you are aware of the conflict.
If you feel that the assistance you receive is in any way unsatisfactory, let me know the date and time as well as the problem you encountered.
Schedule of Topics
(Note: This schedule is tentative and may be revised at a later date.)
|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)|