Engineering Differential Equations 92.236 section 203 Fall 2009

Exam Review Sheets, Including Practice Exams

1. Exam # 1 Review Sheet

2. Exam # 2 Review Sheet

3. Exam # 3 Review Sheet

4. Final Exam Review Sheet
   
   

Solution Sheets for Practice Exams

1. Solutions to Practice Exam # 1

2. Solutions to Practice Exam # 2

3. Solutions to Practice Exam # 3

4. Solutions to Practice Final Exam
   
    

Take-Home Parts of Exams

1. Take-home part of Exam 1.

2. Take-home part of Exam 2.

3. Take-home part of Exam 3.

Project

Here is the project description.  Here are a sample project description and a sample report.

Homework for Sections 2.4, 2.6, 4.3

1. Section 2.4 homework handout

2. Section 2.6 homework handout

3. Section 4.3 homework handout

 
MATLAB Handouts

1. Handout on Graphing (September 10)

2. Handout on Symbolic Utilities (September 17)

3. Handout on Numerical Methods (October 1). You will also need Dr. White's scripts euler.m and rk4.m and the homework assignments for section 2.4 and section 2.6.

4. Handout on Slope Fields (October 15)    You will also need Dr. John Polking's script dfield6.m. In case you don't have your textbook with you, the homework assignment on slope fields includes problems 1, 2, 7, and 9 from section 1.3.

5. Handout on Phase Planes (October 29)    You will also need Dr. John Polking's script pplane6.m

6. Handout on Damped Response of a Mass-Spring System (November 3). You will also need the files damped_response_2.m and damped_response_2.fig

7. Handout on Numerical Methods for Systems (November 12)  to be used for the section 4.3 homework.  You will also need Dr. White's script rk4.m

8. Handout on Symbolic Laplace Transform Utilities (December 3)

9. Handout on Matrix Algebra Commands

    

Class Handouts

1. Solution method for first order linear equations

2. Solving first order equations

3. Solving second order constant coefficient equations

4. The Method of Undetermined Coefficients

5. Example of the Method of Variation of Parameters

6. Examples of forced motion

7. Example of forced motion with discontinuous forcing term

8. Example of forced motion with an impulse force

Challenge Problems

1. A friend of mine in college claimed that hot water freezes faster than cold water. His reasoning was that hot water loses heat at a faster rate than cold water, so if you put a container of hot water and a container of cold water in a freezer at the same time, the hot water will cool down faster and will freeze first. What does our heating/cooling model have to say about my friend's theory?

2. The Snowplow Problem: One night it started snowing at a steady rate. A snowplow started out at midnight. At 1 a.m., it had gone 2 miles. At 2 a.m., it had gone another mile. What time did it start snowing?

3. An interesting application of radioactive dating.

4. The total energy E of a mass-spring system is given by E = ½ m v² + ½ k x². Show that E is constant for an undamped, unforced system, and show that E is a decreasing function of time for a damped, unforced system.