Math 385 (Differential Equations and Orthogonal Functions) Spring 2007

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).

Links

Current course grades : click on `Score Reports'

Homework assignment for the current week

Course announcements

Lecture Log

Contents

• Instructor information
• Course information
• Textbook and computing resources
• Homework, quizzes and tests
• Grading Policy
• Policies regarding late assignments
• Deadlines
• Tutoring room
• Anonymous student feedback
• List of topics to be covered and schedule of lectures and labs

• Instructor: Prof. Jeremy Tyson
• Office Location: 330 Illini Hall
• Office Phone: 244-4132
• Email: tyson@math.uiuc.edu
• Office Hours: Mon 3-4, Wed 1-2, Thu 1-2

• Lecture Times: MonWedFri 9:00-9:50
• Lecture Location: 156 Henry Building
• Course web site: http://www.math.uiuc.edu/~tyson/385s07.html.

  Announcements of quizzes, tests, and general information related to the class can be found at http://www.math.uiuc.edu/~tyson/385s07announcements.html

• Course Text: Differential Equations and Boundary Value Problems (third edition), by C. H. Edwards, Jr. and D. E. Penney (Prentice-Hall, Inc.), 3rd edition, 2004.
• Computer resources:
  • IODE: an interactive differential equations program developed by Peter Brinkmann, Robert Jerrard and Richard Laugesen of the University of Illinois.
  • 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 each Friday. They can be turned in during class or in the envelope outside my office door by 12:00 noon on the due date. The homework assignments are all posted at http://www.math.uiuc.edu/~tyson/385s07hw.html. Some of the homework assignments will require you to use the software package IODE (see below). Each week the TA will grade a selected number of the submitted homework problems.

  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.)

• 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/385s07announcements.html at least one class period in advance.
• Computer labs and projects: This section of Math 385 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	15%
  IODE projects	10%
  Quizzes	10%
  First Midterm	20%
  Second Midterm	20%
  Final	25%

• 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, for documented 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.

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• 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.
• Student feedback: I am interested in your opinions on how the course is progressing, aspects which you feel are particularly helpful and those which you feel could be improved. You may submit comments regarding the course or regarding the IODE computer labs.

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• Deadlines: The last day to add this course is Monday January 29. The last day to drop this course is Friday March 9. Engineering students must have the approval of the Dean to drop this course at any time.

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• Tutoring room: The Math department provides free tutoring for Math 385. In Spring 2007 the hours and location are: Mon-Thu 3-5pm, 145 Altgeld Hall; Mon-Thu 7-9pm, 241 Altgeld Hall.

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

FINAL EXAM IS SATURDAY MAY 5 FROM 8:00 TO 11:00 AM