University of Notre Dame
Aerospace and Mechanical Engineering
AME 301: Differential Equations, Control and Vibrations Syllabus
Instructors:
Teaching Assistants:
 Neil Petroff
 Baoyang Deng
 Abigail Mitchell
 Tatiana Pimenova
Course Web Page:
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:
 Second Order Linear Equations
 Introduction/Review (1 class)*
 Fundamental solution of the homogeneous equation (1 class)*
 Homogeneous equations with constant coefficients (1 class)*
 Unforced damped and undamped vibrations (2 classes)
 Equivalent spring and damper systems (2 classes)
 Linearization of nonlinear systems (1 class)
 Stability of linearized nonlinear systems (1 class)
 Energy methods (2 classes)
 Nonhomogeneous equations (2 classes)
 Forced damped and undamped vibrations (3 classes)
 System response and force transmission (3 classes)
 Transient response under harmonic and general forcing (2 classes)
 Nonviscous damping: hysteretic and coulomb friction (3 classes)
 Introduction to Feedback Control (second order systems)
 First order plant response under PID control (1 class)
 Definition of Laplace transform (1 class)
 Solutions to initial value problems (1 class)
 Block diagrams and block diagram algebra (1 class)
 Step response versus pole locations (1 class)
 Time domain specifications for feedback problems (1 class)
 Effects of zeros and additional poles (1 class)
 Routh's stability criterion (1 class)
 Numerical Methods
 Euler method (1 class)
 Error analysis (1 class)
 Improved Euler method (1 class)
 Three term Taylor series method (1 class)
 RungeKutta method (2 classes)
 Exams (2 classes)
Return to the AME 301 Homepage.
Last updated: August 23, 2003
B. Goodwine (jgoodwin@nd.edu)