**University of Notre Dame**

Aerospace and Mechanical Engineering

Aerospace and Mechanical Engineering

AME 30314: Differential Equations, Vibrations and Control I

Instructor:

- Bill Goodwine

Office: 376 Fitzpatrick

Email: goodwine@controls.ame.nd.edu

- Peter Sutcliffe, Hessert, psutclif@nd.edu
- Piyush Ranade, Hessert, pranade@nd.edu
- Mohammed Kamel, Hessert, mkamel@nd.edu
- Dewen Yushu, Cushing, dyushu@nd.edu
- Sebastian Sensale, Fitzpatrick/Cushing, ssensale@nd.edu
- Zhe Feng, Cushing, zfeng1@nd.edu

- 141 DeBartolo Hall

MWF 9:25-10:15

- Goodwine: Mondays 4:00 - 5:30, Tuesdays, 4:45-5:30pm, 376 Fitzpatrick
- Possible TA office hours TBA

- The final grade will be based on homework sets and four exams with the following distribution:
- Homework (10%)
- Exam 1 (20%): Tuesday, September 15, 2015, 8:00-9:15am, 141 DBRT
- Exam 2 (20%): Thursday, October 15, 2015, 8:00-9:15am, 141 DBRT
- Exam 3 (20%): Tuesday, December 1, 2015, 8:00-9:15am, 141 DBRT
- Final exam (30%): Wednesday, December 16, 2015, 1:45-3:45,141 DBRT

- Any student missing an examination without an excuse from the Office of Student Affairs will receive a grade of zero for that exam.
- Guaranteed grades: if your score satisfies these conditions, you will receive the indicated grade
*or better*.- (overall grade > mean + 1.5 stdev) OR (overall grade > 90%): A-
- (overall grade > mean + 0.5 stdev) OR (overall grade > 80%): B-
- (overall grade > mean - 1.0 stdev) OR (overall grade > 70%): C-
- (overall grade > mean - 2.0 stdev) OR (overall grade > 60%): D
- (overall grade < mean - 2.0 stdev): F

- I am happy to regrade anything that was not properly graded. Write on the front what you want me to regrade and why you think it was not properly graded. Especially with exams, please consult the grading method that I post for the exam before submitting a regrade request.

- Homework sets will be assigned weekly and will be due before class on Wednesdays.
*Late homework will not be accepted without permission from the instructor***prior**to the time it is due. - Students must submit their homeworks with their Notre Dame ID number (ndID) written on the homework. You may put your name on it if you wish, but they will not be graded without your ndID number.
- 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. Submitting material that does not reflect the results of your own efforts and does not substantively reflect your understanding of the subject matter at the time it was created is a violation of the Academic Code of Honor.
- You may not consult homework solutions from prior years, from online sources, or any other solutions. Doing so is a violation of the Academic Code of Honor.
- Examples of allowed activities include:
- working on homeworks and projects as a group provided every member of the group submits material that is consistent with paragraph 3 above;
- obtaining help debugging computer programs provided that the computer program submitted is consistent with paragraph 3 above; and,
- consulting another person regarding any aspect of a homework assignment provided that what is ultimately submitted is consistent with paragraph 3 above.

- Examples of dishonest activities include:
- unless expressly allowed by the instructor, submitting material that is not entirely the result of your own intellectual effort;
- 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;
- signing in another person when attendance is taken;
- submitting material that is copied, wholly or in part, in any form;
- viewing, downloading, copying, reviewing or obtaining homework solutions from this course from any previous year; and,
**any**activity not expressly allowed above that violates either the letter or spirit of the University Academic Code of Honor.

- Because collaboration is encouraged, there is a fine line between allowed and disallowed activities when completing homework assignments. If you have any doubt regarding whether the degree or substance of your collaboration was allowed, then simply
*disclose*it on the homework. In such a case, the activity*may*result in a lowered grade on that work, but will*not*be treated as a violation of the Academic Code of Honor. - All students must familiarize themselves with the Honor Code on the University’s website and pledge to observe its provisions in all written and oral work, including oral presentations, quizzes and exams, and drafts and final versions of essays. Students will not give or receive aid on exams. This includes, but is not limited to, viewing the exams of others, sharing answers with others, and making unauthorized use of books or notes while taking the exam. Students must abide by the homework policy described above.
- Independent of the Honor Code, submitting work that is a result of your own effort and representative of your understanding is an instruction for all homeworks and exams. Any work submitted that is not in accordance with this instruction will receive a grade of zero.

- I consider it part of my job to make it as easy as possible for you to develop a mature and sophisticated understanding of differential equations, their solution methods and the role they play in engineering. As such, I am happy to answer any and all questions you may have (or to direct you to others, if I think they could do so better) as many times as is necessary to help further this goal, provided that you meet your similar obligation to make a substantive and mature effort to achieve the same goal. Hence:
- If you regularly attend class, are not disruptive, make an effort to make class time productive for yourself and others, outside of class study the material and regularly complete the assignments, I will make every effort to promptly respond to any communication addressed to me.
- If you skip class, are generally disruptive, inattentive, texting, surfing the web, completing other coursework, reading the paper, doing the crossword puzzle, etc., I will answer your questions at a time that is convenient for me, which may be never. If you ask questions regarding administrative matters, e.g., test coverage, that I already announced in class, I will not answer them.

- The required text for this course is
*Engineering Differential Equations: Theory and Applications,*by Bill Goodwine, errata. - A highly recommended reference text for the course is
*Elementary Differential Equations and Boundary Value Problems*by William E. Boyce and Richard C. DiPrima, 8th Edition. - A recommended reference on vibrations is
*Mechanical Vibrations*by J. P. DenHartog ( $20 ).

This course covers the following broad topics:

- a review of solution methods for first order ordinary differential equations and second order, constant coefficient, linear ordinary differential equations;
- single degree of freedom oscillations (undamped, damped, unforced and forced);
- a brief introduction to feedback control;
- numerical methods for differential equations;
- separation of variables for partial differential equations, with emphasis on the wave equation, heat equation and Laplace's equation; and,
- introduction to nonlinear systems.