Math 285 Intro. to Differential Equations
Section N1, TR 10:30 - 11:50
140 Burrill Hall
M. Burak Erdogan

Study problems and announcements

Contact Info:
 Office: 369 Altgeld Hall
 Phone: 217 265 6761
 e-mail: berdogan@
 Webpage: www.math.uiuc.edu/~berdogan (there is a link to the course webpage)

Office hours: W,R 9-10:30

Required textbook: Edwards & Penney, Differential equations and boundary value problems: Computing and modeling, Custom Edition for the UIUC, Pearson Custom Publishing, 2008. This edition is taken from the Fourth Edition of Edwards & Penney which is the standard text for Math 286. If you prefer you can use the full 4th edition.

Grading: Weekly quizzes (25%), 2 midterm exams (20% each) and final (35%). (Please do NOT request an alteration for yourself in these percentages). No make-up exams or quizzes.

Study problems and quizzes: Every Thursday, I will post study problems on the course webpage. The solutions will be posted on the next Tuesday, and there will be an in class quiz (from the study problems) on Thursday. You should work on the problems before the solutions are posted and compare your solutions with the posted ones to be ready for  the quiz on Thursday. In the midterm weeks there will be study problems but no quiz. The worst two quiz grades will be dropped. Absolutely no make-up quizzes. 

Exams:  There will be two in class midterm exams and an in class Final. The midterms are on Thursday, October 2nd and Thursday, November 13th. The final is on Wednesday, December 17th between 8:00am and 11:00am.

Outline: 

Chapter 1. First Order Differential Equations (6 lectures)

1.1 Differential Equations and Mathematical Models

1.2 Integrals as General and Particular Solutions

1.3 Slope Fields and Solution Curves

1.4 Separable Equations and Applications

1.5 Linear First Order Equations

1.6 Substitution Methods and Exact Equations

Chapter 2. Mathematical Models and Numerical Methods (2 lectures)

2.1 Population Models

2.3 Acceleration-Velocity Models

Chapter 3. Linear Equations of Higher Order (14 lectures)

3.1 Introduction: Second-Order Linear Equations

3.2 General Solutions of Linear Equations (3)

3.3 Homogeneous Equations with Constant Coefficients (2)

3.4 Mechanical Vibrations (2)

3.5 Nonhomogeneous Equations and Undetermined Coefficients (3) 

3.6 Forced Oscillations and Resonance (2)

3.8 Endpoint Problems and Eigenvalues (2)

Chapter 9. Fourier Series Methods (12 lectures)

9.1 Periodic Functions and Trigonometric Series (3)

9.2 General Fourier Series and Convergence (1)

9.3 Fourier Sine and Cose Series (1)

9.4 Applications of Fourier Series (1)

9.5 Heat Conduction and Separation of Variables (2)

9.6 Vibrating Strings and the One-Dimensional Wave Equation (2)

9.7 Steady-State Temperature and Laplace's Equation (2) 

Chapter 10. Eigenvalues and Boundary Value Problems (5 lectures)

10.1 Sturm-Liouville Problems and Eigenfunction Expansions (2)

10.2 Applications of Eigenfunction Series (2)

10.3 Steady Periodic Solutions and Natural Frequencies (1)

Examinations, review and leeway (5 lectures)