University of Notre Dame
Aerospace and Mechanical Engineering

AME 301: Differential Equations, Control and Vibrations Syllabus

Instructors:

Teaching Assistants:

Course Web Page:

Grading:

The final grade will be based on homework sets and three exams.

Homework policy:

Course text and references:

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)

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