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
Contents
Announcements of quizzes, tests, and general information related to the class can be found at https://math.uiuc.edu/~tyson/385s07announcements.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.)
NonEngineering 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.
Homework  15% 
IODE projects  10% 
Quizzes  10% 
First Midterm  20% 
Second Midterm  20% 
Final  25% 
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 makeup 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.
(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 FirstOrder 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: SecondOrder 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: Steadystate 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