# AME 301: Differential Equations, Control and Vibrations Syllabus

### Teaching Assistants:

• Neil Petroff
• Baoyang Deng
• Abigail Mitchell
• Office: TBA
• Email:
• Tatiana Pimenova
• Office: TBA
• Email:

### Grading:

The final grade will be based on homework sets and three exams.
• Homework (15%)
Homework sets will be assigned weekly and will be due before the beginning of class on Wednesdays. Late homework will not be accepted without prior permission from the instructor.
• Exam 1 (25%): Wednesday, October 8, 2003.
• Exam 2 (25%): Wednesday, November 19, 2003.
• Final exam (35%): Thursday, December 18, 2003.

### Homework policy:

• Collaboration on homework assignments in encouraged. You may consult outside reference materials, other students, the TAs, or the instructor. However, all solutions that are handed in should reflect your understanding of the subject matter at the time of writing.

### Course text and references:

• The required text for the course is Elementary Differential Equations 7th Edition, by William E. Boyce and Richard C. DiPrima.

### Course outline:

1. Second Order Linear Equations
1. Introduction/Review (1 class)*
2. Fundamental solution of the homogeneous equation (1 class)*
3. Homogeneous equations with constant coefficients (1 class)*
4. Unforced damped and undamped vibrations (2 classes)
5. Equivalent spring and damper systems (2 classes)
6. Linearization of nonlinear systems (1 class)
7. Stability of linearized nonlinear systems (1 class)
8. Energy methods (2 classes)
9. Nonhomogeneous equations (2 classes)
10. Forced damped and undamped vibrations (3 classes)
11. System response and force transmission (3 classes)
12. Transient response under harmonic and general forcing (2 classes)
13. Non-viscous damping: hysteretic and coulomb friction (3 classes)
2. Introduction to Feedback Control (second order systems)
1. First order plant response under PID control (1 class)
2. Definition of Laplace transform (1 class)
3. Solutions to initial value problems (1 class)
4. Block diagrams and block diagram algebra (1 class)
5. Step response versus pole locations (1 class)
6. Time domain specifications for feedback problems (1 class)
7. Effects of zeros and additional poles (1 class)
8. Routh's stability criterion (1 class)
3. Numerical Methods
1. Euler method (1 class)
2. Error analysis (1 class)
3. Improved Euler method (1 class)
4. Three term Taylor series method (1 class)
5. Runge-Kutta method (2 classes)
4. Exams (2 classes)

Last updated: August 23, 2003
B. Goodwine (jgoodwin@nd.edu)