AME 302: Differential Equations, Control and Vibrations II Syllabus

Instructor:

Teaching Assistants:

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

Homework (10%)
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 (20%): Wednesday, February 11, 2004.
Exam 2 (20%): Wednesday, March 24, 2004.
Exam 3 (20%): Monday, April 26, 2004
Final exam (30%): TBA.

Collaboration on homework assignments in encouraged. Unless otherwise prohibited, you may consult outside reference materials, other students, the TAs, or the instructor. However, all material that is submitted must be the result of your own individual effort and accurately and substantively reflect your understanding of the subject matter at the time of writing.
Examples of allowed activities:
1. working on homeworks and projects as a group provided every member of the group submits material that is consistent with paragraph 1 above;
2. obtaining help debugging computer programs provided that the computer program submitted is consistent with paragraph 1 above.
3. consulting another person regarding any aspect of a homework assignment provided that what is ultimately submitted is consistent with paragraph 1 above.
Examples of dishonest activities:
1. unless expressly allowed by the instructor, submitting material that is not entirely the result of your own intellectual effort;
2. submitting material that is intentionally misleading such as plots or graphs that were not generated by an accompanying computer code listing, a computer code listing that is purported to be correct that is not or a homework problem that has the correct answer that does not result from the work preceding it; and,
3. submitting material that is copied, wholly or in part, in any form.

The required text for the course is Elementary Differential Equations 7th Edition, by William E. Boyce and Richard C. DiPrima.
A recommended reference on vibrations is Mechanical Vibrations by J. P. Den Hartog ($16).
A recommended reference on control theory is Schaum's Outline of Feedback and Control Systems by Joseph Distefano, Ivan J. Williams, Joseph J., III DiStefano an Allen Stubberud. ($12).

Systems of First Order Linear Equations
1. Linear Independence, Eigenvalues and Eigenvectors (1 class)*
2. Homogeneous Linear Systems (1 class)
3. Complex Eigenvalues (1 class)
4. Repeated Eigenvalues (1 class)
5. Two degree of freedom vibrations
  1. unforced vibration and fundamental modes (2 classes)
  2. Lagrangian dynamics (3 classes)
  3. principal coordinates (2 classes)
  4. Forced vibration, absorbers and force transmission (2 classes)
6. Application to controls
  1. basic pole placement in state space (2 classes)
  2. s-plane connection to state space representation (1 class)
  3. root locus method
    1. sketching (2 classes)
    2. selecting gains from root locus (1 class)
    3. lead compensation (1 class)
    4. lag compensation (1 class)
    5. time delay and Pade approximation (1 class)
  4. frequency domain methods
    1. Bode plots
      1. sketching (2 classes)
      2. stability and steady state errors (1 class)
      3. lead compensation (1 class)
      4. lag compensation (1 class)
    2. Nyquist plots (2 classes)
Partial Differential Equations
1. Heat Conduction and Separation of Variables (1 class)
2. Fourier Series (2 classes)
3. Even and odd functions (1 class)
4. Wave equation, axial, torsional and transverse vibrations (4 classes)
Exams (3 classes)

* Indicates review of material from MATH 228

Last updated: January 14, 2004
B. Goodwine (jgoodwin@nd.edu)