AME 30314 Course Syllabus

Read this very carefully for course policies and procedures and to find some useful handouts.
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AME 30314 Course Syllabus

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University of Notre Dame
Aerospace and Mechanical Engineering

AME 30314: Differential Equations, Vibrations and Control I

Instructor:
  • Bill Goodwine
    Office: 367 Fitzpatrick
    Email: goodwine@controls.ame.nd.edu
    Office Hours: Tuesdays, 8:00 - 9:30pm except September 5, October 17, and December 5. On those dates office hours will be from 2:00 - 3:30pm
TAs: Time and Place:
  • Room 102 DBRT
    11:45 - 12:35 MWF
Course Web Page: Grading:
  • The final grade will be based on homework sets and three exams:
    1. Homework (10%)
    2. Exam 1 (25%): Wednesday, October 4, 2006.
    3. Exam 2 (25%): Wednesday, November 15, 2006.
    4. Final exam (40%): TBA
  • Guaranteed grades:
    1. (overall grade > mean + 1.5 stdev) OR (overall grade > 90%): A/A-
    2. (overall grade > mean + 0.5 stdev) OR (overall grade > 80%): B+/B
    3. (overall grade > mean - 0.5 stdev) OR (overall grade > 70%): B-/C+/C
    4. (overall grade > mean - 1.5 stdev) OR (overall grade > 60%): C-/D+
    5. overall grade > mean - 2.0 stdev: D/D-
    6. overall grade < mean - 2.0 stdev: F
Homework Policy:
  1. Homework sets will be assigned weekly and will be due before the beginning of class on Wednesdays. Late homework will not be accepted without permission from the instructor prior to the time it is due.
  2. 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.
  3. Examples of allowed activities include:
    1. working on homeworks and projects as a group provided every member of the group submits material that is consistent with paragraph 2 above;
    2. obtaining help debugging computer programs provided that the computer program submitted is consistent with paragraph 2 above.
    3. consulting another person regarding any aspect of a homework assignment provided that what is ultimately submitted is consistent with paragraph 2 above.
  4. Examples of dishonest activities include:
    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;
    3. submitting material that is copied, wholly or in part, in any form; or,
    4. any activity not expressly allowed above that violates either the letter or spirit of the University Academic Code of Honor.
Course Text and References:
  1. The required text for the course is Elementary Differential Equations and Boundary Value Problems by William E. Boyce and Richard C. DiPrima, 8th Edition.
  2. A very highly recommended text on C programming is the C Programming Language by Brian W. Kernighan and Dennis Ritchie, 2nd Edition ($44).
  3. A recommended reference on vibrations is Mechanical Vibrations by J. P. DenHartog ($18).
  4. 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. ($6).
Subject Outline:
  1. Second Order Linear Systems
    1. Introduction and review*
    2. Linear equations, homogeneous equation*, fundamental solution, equations with constant coefficients*
    3. Inhomogeneous equations
    4. Nonlinear systems, linearization, phase plane
    5. Stability of linearized nonlinear systems
    6. Boundary value problems and Sturm-Liouville theory
  2. Single Degree of Freedom Vibrations
    1. Unforced damped and undamped vibrations
    2. Equivalent spring and damper systems
    3. Forced damped and undamped vibrations
    4. Energy methods
    5. System response and force transmission
    6. Transient response under harmonic and general forcing
    7. Hysteresis, Coulomb friction and nonlinear vibrations
  3. Partial Differential Equations
    1. Elliptic, parabolic and hyperbolic equations, separation of variables
    2. Fourier series
    3. Even and odd functions
    4. Laplace's equation
    5. Heat equation
    6. Wave equation
  4. Numerical Methods
    1. Euler method
    2. Error analysis
    3. Improved Euler method
    4. Three-term Taylor series method
    5. Runge-Kutta method
    6. Finite-difference method
* indicates review material.

Weekly Schedule:
  1. Review B&D chapters 1 and 2, start review of chapter 3
  2. Finish review of B&D Chapter 3, sections 2.7, 8.1 and 8.2
  3. B&D sections 8.3 - 8.6
  4. B&D sections 2.5 and 9.1 - 9.4
  5. B&D sections 9.5 - 9.8
  6. DenHartog chapter 1 and sections 2.1 - 2.3 (Exam 1)
  7. DenHartog sections 2.4 - 2.8
  8. Energy methods, system and transient response
  9. Hysteresis, friction and nonlinear damping and introduction to PID control
  10. B&D sections 10.1 - 10.5
  11. B&D sections 10.6 and 10.7
  12. B&D section 10.8 and the finite difference method for partial differential equations (Exam 2)
  13. B&D sections 11.1 - 11.2
  14. B&D sections 11.3
Bill Goodwine, 376 Fitzpatrick
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