ME6758 Numerical Methods in Mechanical Engineering

Fall 2005

Professor Al Ferri

Office: J. Erskine Love Jr. Manufacturing Building (MRDC-II), Rm 107 Phone: (404)-894-7403, (404)-894-8496 (FAX) Email Address: al.ferri@me.gatech.edu Office Hours: Tuesdays, 9:30-11am Class Meeting Time/Place: MWF, 2:05-2:55pm, Rm 110, Sustainable Engineering Building (SEB) Textbook: Numerical Methods, 3rd Edition, Faires and Burden, Brooks/Cole Publishing Co., 2003, ISBN 0-534-40761-7, Approximate Price: $119.10 (New), $89.35 (Used) TA: Nsikan Udoyen Office Hours: 11am-1pm on Mondays, Rm 267 MaRC Building

Course Information

Class Syllabus

Prerequisite: Graduate Standing

Course Catalog Description: 

Numerical methods for solution of engineering problems; initial, eigenvalue, and boundary value problems; computational stability for ordinary and linear partial differential equations. Crosslisted with NRE and HP 6758

Announcements/New Items:

• Announcement 1: Homework assignment 1 is now available.
• Announcement 2: Matlab Example showing divergence of result as the matrix size increases..
• Announcement 3: Example of ill-conditioning: Tapered Rod.
• Announcement 4: Starting on MONDAY, 8/29/05 the class will be moved to Rm 110 of the Sustainable Engineering Building (SEB). Unfortunately, Friday's class (8/26/05) will still have to be held in ESM 210- BYOC (Bring Your Own Chair!).
• Announcement 5: Homework assignment 1 has been modified slightly- please see Revised Version
• Announcement 6: On HW1, problem 3, part (c), solve the system of equations "exactly" (using the full precision of the computer) and then re-solve for x and y using 4-digit arithmetic. The absolute error is the difference between the "exact" answer and the one you calculated using 4-digits all the way through the calculation. The relative error is the percent difference between the "exact" answers for x and y and the 4-digit approximate answers.
• Announcement 7: The TA, Nsikan Udoyen, will have office hours from 11am-1pm on Mondays in his office, Rm 267 of the MaRC Building (just north of the Love building, just west of MRDC-I).
• Announcement 8: Distance-Learning (DL) students: Because the lectures in ME6758 are being distributed over the internet (as opposed to video-tapes) the delay between on-campus due-dates/test-dates will be ONE (1) WEEK. Eg., HW1 which is due on Weds, 8/31/05 for on-campus students will be due on Weds, 9/7/05, etc.
• Announcement 9: Here are some notes on condition number of functions and algorithms from Conte and de Boor, Elementary Numerical Analysis: An Algorithmic Approach, 3rd Edition, McGraw Hill, 1980.
• Announcement 10: Here is an m-file that shows the workings of the Modified False Position Method.
• Announcement 11: Homework assignment 2 is now available.
• Announcement 12: Here is a link to an excellent site that explains Floating Point Numbers. It clears up a lot of confusion regarding the case where the characteristic is all zeros or all ones. It also explains how "zero" and "infinity" are handled in the IEEE standard.
• Announcement 13: Since there is no lecture on Monday (9/5/05), there will not be sufficient time to cover Aitken's del-squarred method. Therefore, Problems 1 and 2 on HW2 have been increased to 3 points each and Problem 5 is now Extra Credit.
• Announcement 14: Homework assignment 3 is now available.
• Announcement 15: Powerpoint presentation on Netwon's Interpolating Polynomials.
• Announcement 16: Error in HW3: The Elastic modulus of steel should be 200e+9 N/m^2 (not 200e6); also the units of the density, rho, should be kg/m^3.
• Announcement 17: Homework assignment 4 is now available.
• Announcement 18: Powerpoint presentation on Richardson Extrapolation, Romberg Integration
• Announcement 19: Extra Problems on numerical integration. You should treat this as a homework assignment that will not be collected.
• Announcement 20: Test 1 has been re-scheduled for Friday, September 30, for on-campus students. The test will be closed-book and closed-notes, but you are allowed to bring in a single 8.5x11-inch sheet of paper on which you can write whatever information that you find helpful (formulas, examples, notes, etc.) You may use both sides of the sheet of paper but everything on your sheet MUST BE HANDWRITTEN: NO PHOTOCOPIES. You must turn in your sheet with your test. Calculators will be allowed. The test will cover the material through Chapter 4 of the text, and through HW 4.
• Announcement 21: Students can access taped lectures from webct: http://webct.gatech.edu.
• Announcement 22: Homework assignment 5 is now available.
• Announcement 23: Homework solutions 1 through 4 are now available in the Table below.
• Announcement 24: Test 1 Distribution, ME/NRE6758 SectionA.
• Announcement 25: Homework assignment 6 is now available.
• Announcement 26: Homework assignment 7 is now available.
• Announcement 27: Homework solution 5 is now available in the Table below.
• Announcement 28: Homework assignment 8 is now available.
• Announcement 29: Homework solution 6 is now available in the Table below.
• Announcement 30: Homework solution 7 is now available in the Table below.
• Announcement 31: Here are some extra problems on iterative solutions.
• Announcement 32: Test 2 for on-campus students will be on Friday, 11/11/05. (The test must be completed on or before 11/18/05 for Distance-Learning students). The test will be closed-book, closed-notes. You are allowed to bring 2 formula sheets (two-sided, 8.5x11inches) which MUST BE HANDWRITTEN. You are allowed to use a calculator. The test will be 50 minutes in length and cover the material since the last test. In particular, it will cover material on numerical solution of initial value problems (Euler, Runge-Kutta, Adams, implicit, explicit, etc.), solution of linear systems of equations (Gaussian elimination, LU decomposition) and iterative solution techniques (stationary-iterative solvers, Jacobi iteration, Gauss-Seidel, SOR, iterative refinement, etc.). This is essentially the material from Chapters 5, 6, and 7 of the text, and from homework assignments 5 through 8.
• Announcement 33: Test 1 solution
• Announcement 34: Presentation on Legendre polynomials (corrected).
• Announcement 35: Homework solution 8 is now available in the Table below.
• Announcement 36: Homework assignment 9 is now available.
• Announcement 37: Here is a pdf document that describes in detail why the recursion relation used in the generation of Legendre polynomials produces an orthogonal set of functions.
• Announcement 38: Homework assignment 10 is now available.
• Announcement 39: Test 2 Distribution, ME/NRE6758 SectionA.
• Announcement 40: Homework assignment 11 is now available.
• Announcement 41: The Solution to Test 2 is available.
• Announcement 42: Homework assignment 12 is now available. This assignement will not be collected!
• Announcement 43: Powerpoint presentation on FD solutions to elliptic PDE's.
• Announcement 44: Homework solutions through HW#11 are available in the table below
• Announcement 45: Powerpoint presentation on FD solutions to parabolic PDE's.
• Announcement 46: (Corrected) Homework solution 12 is now available in the Table below.
• Announcement 47: The Final Exam in ME6758 for On-Campus Students will take place at 11:30am, Weds, 12/13/05, in the usual lecture room (Rm 110, SEB). For Distance-Learning students, the Final Exam will take place oin or before Weds, December 21. The exam will be closed-book and closed notes, and counts for 30% of your cumulative grade. You are allowed to use a calculator. Additionally, you are allowed to bring three 8.5x11 inch sheets of paper (two-sided) on which you can HANDWRITE anything you feel would be helpful. The exam will focus on the material since the last test. As stated in class, Anything from Homework Solutions 9 through 12 is fair game, as is any material covered in class, or found at the class website in Announcements 34 on.
• Announcement 48: The Course Instructor Online Survey can be accessed at www.coursesurvey.gatech.edu The survey can be accessed until 11:59pm on Sunday, December 18. Please let me know what you think of the course this semester.
• Announcement 49: The Solution to Final Exam is available.
• Announcement 50:
• Announcement 51:
• Announcement 52:
• Announcement 53:

Assignments

Homework will be collected and graded. Working in groups is allowed so long as it is done responsibly. Solutions to the homework will be passed out along with the returned, graded assignments. It is your responsibility to review these solutions in detail and to compare them with your returned homework assignments. Use of computers in homework problems is strongly encouraged; some homework assignments can not be completed without a computer.

To get the assignment, click on the number in the first column. Links to the solutions are posted in last column when they are available.

Assn. #	Description	Due Date	Solutions
1	Computer precision and condition of algorithms	8/31/05	available
2	Root solving	9/7/05	available
3	Interpolation	9/14/05	available
4	Numerical Integration	9/21/05	available
5	Initial-value problems	10/12/05	available
6	Gaussian elimination and LU decomposition	10/19/05	available
7	LU decomposition and matrix condition number	10/26/05	available
8	Iterative solution techniques	11/2/05	available
9	Least-squares	11/18/05	available
10	FD solutions of BVP's	11/23/05	available
11	Shooting methods and variational methods	12/2/05	available
12	FD solutions of PDE's	NOT COLLECTED	available
13
14
15

Grading Policy:

Test 1 (FRIDAY, SEPTEMBER 30) 25%
Test 2 (Weds, November 9) 25%
Final Exam (Weds, December 14, 2005, 11:30am-2:20pm) 30%
Homework 20%.

Course Schedule

Resources and References

• Netscape Navigator (obtained from the Netscape home page) or Internet Explorer (obtained from the Microsoft IE home page) to view Web pages.
• MATLAB 5.3, available in ME computer clusters