**University of Notre Dame**

Aerospace and Mechanical Engineering

Aerospace and Mechanical Engineering

AME 60611: Mathematical Methods 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.

- Dayu Lv (email: dlv@nd.edu)
- Joel Jimenez-Lozano (email: jjimene1@nd.edu)

- Room 215 Hayes-Healy

3:00 - 3:50 MWF

- The final grade will be based on homework sets and three exams:
- Homework (30%)
- Exam 1 (15%): Wednesday, October 4, 2006.1
- Exam 2 (15%): Wednesday, November 15, 2006.
- Final exam (40%): TBA

- Guaranteed grades:
- (overall grade > mean + 1.5 stdev) OR (overall grade > 90%): A/A-
- (overall grade > mean + 0.5 stdev) OR (overall grade > 80%): B+/B
- (overall grade > mean - 0.5 stdev) OR (overall grade > 70%): B-/C+/C
- (overall grade > mean - 1.5 stdev) OR (overall grade > 60%): C-/D+
- overall grade > mean - 2.0 stdev: D/D-
- overall grade < mean - 2.0 stdev: F

- Homework sets will be assigned weekly and will be due before the beginning of class on Thursdays.
*Late homework will not be accepted without permission from the instructor***prior**to the time it is due. - 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 include:
- working on homeworks and projects as a group provided every member of the group submits material that is consistent with paragraph 2 above;
- obtaining help debugging computer programs provided that the computer program submitted is consistent with paragraph 2 above.
- consulting another person regarding any aspect of a homework assignment provided that what is ultimately submitted is consistent with paragraph 2 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;
- submitting material that is copied, wholly or in part, in any form; or,
**any**activity not expressly allowed above that violates either the letter or spirit of the University Academic Code of Honor.

- The required course text is
*Lecture Notes on Mathematical Methods*by Mihir Sen and Joseph M. Powers, available in the AME office for $30. - An electronic version is available on the web at http://www.nd.edu/~powers/ame.60611/M.pdf
- Homework credit will be awarded for anyone who identifies mistakes in the course text.
- The following texts have been placed on reserve in the engineering library.
- R. Aris,
*Vectors, Tensors, and the Basic Equations of Fluid Mechanics* - C.M. Bender and S.A. Orszag,
*Advanced Mathematical Methods for Scientists and Engineering*(recalled) - B. Friedman,
*Principles and Techniques of Applied Mathematics* - M.D. Greenberg,
*Foundations of Applied Mathematics* - G.H. Golub and C.F. van Loan,
*Matrix Computations* - E.J. Hinch,
*Perturbation Methods* - M.W. Hirsch and S. Smale,
*Differential Equations, Dynamical Systems, and Linear Algebra* - M.H. Holmes,
*Introduction to Perturbation Methods* - D.W. Jordan and P. Smith,
*Nonlinear Ordinary Differential Equations* - W. Kaplan,
*Advanced Calculus*(recalled) - R.J. Lopez,
*Advanced Engineering Mathematics*(recalled) - A.J. McConnell,
*Applications of Tensor Analysis* - A.W. Naylor and G.R. Sell,
*Linear Operator Theory in Engineering and Science* - K.F. Riley, M.P. Hobson and S.J. Bence,
*Mathematical Methods for Physics and Engineering*

- R. Aris,

- Between one and two weeks will be dedicated to each of the following subjects.
- Multi-variable calculus
- First order ordinary differential equations
- Linear ordinary differential equations
- Series solution methods
- Orthogonal functions and Fourier series
- Vectors and tensors
- Linear analysis
- Linear algebra
- Dynamical systems