Math 285 (Differential Equations and Orthogonal Functions) Fall 2002

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).

• Instructor information
• Course information
• Textbook and computing resources
• Homework, quizzes and tests
• Homework assignment for the current week
• Course announcements
• Grading Policy
• Policies regarding late assignments
• Deadlines
• Tutoring Room
• List of topics to be covered and schedule of lectures and labs

• Instructor: Prof. Jeremy Tyson
• Office Location: 227B Illini Hall (go through the door for 227 Illini Hall---my office is one of the two offices located inside 227 IH)
• Office Phone: 244-4132
• Email: tyson@math.uiuc.edu
• Office Hours:Mon 3:30-4:30, Tue 1:00-2:00, Wed 10:30-11:30
• Graduate TA:

• Lecture Times: TueThu 9:00-10:20
• Lecture Location: 156 Henry Building
• Course web site: http://www.math.uiuc.edu/~tyson/285f02.html

• Course Text: Differential Equations and Boundary Value Problems (second edition), by C. H. Edwards, Jr. and D. E. Penney (Prentice-Hall, Inc.), 2000.
• Computer resources:
  • IODE: an interactive differential equations program developed by Peter Brinkmann, Robert Jerrard and Richard Laugesen of the University of Illinois.
  • DiffEqWeb: a graphical ordinary differential equation solver written by Simo Kivelä and Mika Spåra of the Helsinki University of Technology.
  • Programs for Euler's method and slope field generation for graphing calculators (Texas Instruments TI-82, TI-85 and Sharp EL-9300, EL 9200).

• Homework: Homework problems will be assigned each week and will be due on Thursdays. They can be turned in during class or in the envelope outside my office door. The homework assignments are all posted at http://www.math.uiuc.edu/~tyson/285f02hw.html. Some of the homework assignments will require you to use the software package IODE (see below).

  Each week the TA will grade a random selection of the submitted homework problems.

• Quizzes: Approximately twice a month there will be a short quiz (covering 2-3 sections of the text). All quizzes will be announced at http://www.math.uiuc.edu/~tyson/285f02announcements.html at least one class period in advance.
• Computer labs and projects: This section of Math 285 will have a computer component, using the free software package IODE. A few times during the semester the class will meet at an Engineering Workstation (EWS) lab, and several homework assignments will require the use of this software. You do not need any prior computing experience for this.

  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.

• Exams: There will be two midterm exams and a cumulative final exam. For the dates, see the schedule.

• Grading Policy: Grades will be computed according to the following percentages:

  Homework (including computer projects)	15%
  Quizzes	10%
  First Midterm (9/26 in class)	20%
  Second Midterm (10/31 in class)	20%
  Final (12/19 8:00-11:00am)	35% (cumulative)

• Policies regarding late assignments: Late homework will be accepted only if arrangements have been made with me before the deadline. However, exceptions can be made in other cases, for example, medical or family emergency. At the end of the semester I will drop the lowest two homework scores.

  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.

• Resources: If you have questions regarding the course material at any time during the semester, you are encouraged to send email, either to myself or to the TA. It is not always easy to explain mathematical concepts via email, however, so if your question is a mathematical one, you should probably ask me in person during my office hours.
• Tutoring Rooms: these rooms are staffed by graduate TA's who are available to answer questions about the course material. The tutoring rooms for this semester are 207 Gregory Hall (Tue-Thu 3-5pm) and 243 Altgeld Hall (Mon-Thu 7-9pm). 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.

• Deadlines: The last day to add this course is Friday, September 13. The last day to drop this course is Friday, October 18. Engineering students must have the approval of the Dean to drop this course at any time.

Schedule of Topics

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