Course Description: We continue to study, develop, and analyze algorithms for obtaining numerical solutions to mathematical problems, with particular emphasis on the numerical solutions of ordinary and partial differential equations. Additional topics like iterative methods for solving linear systems, and homotopy methods for solving non-linear equations will also be discussed.

Software:  We will be using  MATLAB,  a high-level interactive system containing state-of-the-art routines for numerical computation. Matlab stands for "MATrix LABoratory", and it is available on the PC's in the Rood Hall Computing Lab, and some Engineering Labs.  For Rood Hall lab hours see http://www.wmich.edu/math/ASLab/.  On your home computer you may use the freely available Matlab clone, GNU Octave. See http://www.octave.org/ for more details. Binaries for Linux and Windows are available.

Complimentary SIAM Student Memberships: SIAM stands for the Society for Industrial and Applied Mathematics. Because WMU is an institutional member of SIAM, any WMU student majoring in mathematics, engineering or the applied sciences is eligible for free SIAM membership. This entitles you to a discount on all SIAM publications, plus other benefits. Go to http://www.siam.org/about/member.htm and click on Complimentary Student Memberships.

Reading/Self Study: It is important to regularly read the text and work out the Exercises for the Reader woven into each section. Solutions to these exercises are included in Appendix B at the end of the text. Read the text and practice the exercises with care. It is an effective way to build your technical reading and writing skills.

Homework consisting of a mixture of pencil-and- paper problems and computing projects will be regularly assigned and collected. You are strongly advised to start working on hw assignments early. Do not underestimate the difficulty of the assignments or the time you need to complete them. All submitted solutions must be legible, organized, and always include reasoning (whether the problem explicitly calls for it or not). Problems will cover both applied and theoretical aspects of the course. Matlab will be an integral part of several assignments. You are encouraged to discuss homework problems with each other and to learn from each other. Help received from others must be acknowledged by a note at the beginning of your assignment. However, under no circumstances is it acceptable for you to copy each other's work. Academic integrity policies will be strictly enforced. It is important that you follow the Homework Guidelines. You can also find the homework grading policy in the guidelines.

Exams:   A tentative date for the in-class Midterm is Feb 17. A cumulative Final will be held Tue Apr 26, 5 - 7pm. Make-up exams will be permitted only in those cases when a student documents a genuine medical or personal emergency.

Evaluation: Homework:  50%      Midterm:  20%      Final: 30%.   An approximate grading scale is given below:

Important Dates: 
          Fri Jan 14: Registration Closes, Last Day to Drop/Add
          Mon Jan 17:  MLK Day, no classes
          Fri Feb 25: Spirit Day, no classes
          Feb 28 through Mar 4: Spring Recess
          Mon Mar 21:  Last day to Withdraw
          Thurs Apr 21:  Last day of instruction (for this class)
          Tues Apr 26  5 - 7pm, Final Exam (for this class)

Academic Integrity:  You are responsible for making yourself aware of and understanding the policies and procedures in the Graduate  (pp. 26-28) Catalog that pertain to Academic Integrity. These policies include cheating, fabrication, falsification and forgery, multiple submission, plagiarism, complicity and computer misuse. If there is reason to believe you have been involved in academic dishonesty, you will be referred to the Office of Student Conduct. You will be given the opportunity to review the charge(s). If you believe you are not responsible, you will have the opportunity for a hearing. You should consult with me if you are uncertain about an issue of academic honesty prior to the submission of an assignment or test.

Incompletes: Departmental rules will be followed regarding ``I'' (Incomplete) grades. An ``I'' grade may be assigned only when circumstances beyond the student's control prevent completion of a small segment of the course. Incompletes may not be granted under any circumstances when a student is doing unsatisfactory work; such students are advised to withdraw from the course.

Class Fees  help towards the cost of specialized computer software, and contribute towards the support of the computer labs. These fees do not cover all the costs incurred. Please use the printing resources wisely -- do not waste paper.

New University e-mail policy:   The only email address to be used for communication between WMU students and WMU faculty and staff is the email address associated with a BroncoNet ID.  This email address typically takes the form

firstname.middleinitial.lastname@wmich.edu

Students cannot automatically forward email from this address to other addresses.  Students can access this email account or get instructions for obtaining a BroncoNet ID at GoWMU.wmich.edu.

1. You must have a valid WMU ID to use the lab.
2. No food or drinks are allowed in the lab at any time.
3. Think before you print! Do not waste paper.
4. If you notice a hardware or software problem, bring it to the attention of the lab monitor, asking that they take appropriate action, and send me email so I can also report the problem. Your email should identify machine, the nature of the problem, and the time  the problem occurred.
5. Remember to save your personal work on your personal storage device before leaving the lab.

You are encouraged to discuss homework problems with each other and to learn from each other. Help received from others must be acknowledged by a note at the beginning of your assignment. Under no circumstances is it acceptable for you to copy each other's work. See the section on Academic Integrity .

You are strongly advised to do your homework assignments promptly. Problems will cover both numerical and theoretical aspects of the course. Solutions must be legible, organized and always include reasoning (whether the problem explicitly calls for it or not).

Numerical experimentation is an integral part of the course. Its goal is to reinforce and reflect theory, compare and contrast theory with practise, and make numerical and theoretical conjectures.

Here are some tips on what makes a good solution to a problem involving numerical computation. Not all of these may be applicable in very problem:

1. Your Matlab code should either be a script or an m-file, created using the built-in Matlab editor. See Chapter 3 of the Stanoyevitch text.
2. Your code must follow the standard recommendations regarding documentation, comments and indentation.
3. Describe the design of your experiment. If you are comparing Method A with Method B, consider comparing the performance (for example, in terms of efficiency and accuracy) of each of the methods against a standard benchmark. A benchmark could be the exact solution computed by analytical (rather than numerical) means, or it could be a different method (which could be a built-in Matlab function).
4. Describe the test data, and why you chose it. Do the same for any other design parameters.
5. Do NOT submit reams of output. This will almost certainly earn you negative credit.
6. Organize your output in a compact and readable fashion. Use format compact to suppress unnecessary line feeds. Calculate relative errors if appropriate; summarize results in a table.
7. When appropriate, plot your numerical data. Learn about Matlab's subplot command which allows you to display multiple plots in the same graphing window.
8. All output, numerical and graphical, must be annotated, clearly identifying the features of interest. Annotations by hand are okay, even preferable at times.
9. Discussion of your output should be alongside your output. Don't make the reader keep turning pages back and forth.
10. What do you observe? What does the output suggest? Can you explain your observations?
11. What conclusions can you draw from your experiments? Why? How does theory compare with practise? For example, how do the mathematically exact solutions compare with the numerical ones? Or, can you prove by analytical means the patterns you've observed or been led to conjecture by numerical means?
12. Does your experiment suggest directions for further exploration? New conjectures? Generalizations? Include any progress made on such investigations. You are encouraged to extend exercises in this manner, and carry out your own on-going investigations during the semester.

1. To save output to a file, you can use Matlab's diary command. To learn more, type help diary at the Matlab prompt.
2. Creating special matrices:
   >> help ones
   >> help zeros
   >> help eye
   >> help diag
   Example: >> n = 5; a = 5*eye(n) - 2*diag(ones(n-1,1),1) + 3*diag(ones(n-1,1),-1);
3. Formats: >> help format
   Useful formats are: format short, format long, format rat.
   Always use format compact when printing to save paper. Don't confuse format compact with format short .
4. Entering a polynomial: >> help poly
   Finding its roots: >> help roots
   Finding its derivative: >> help polyder
   Evaluating a polynomial: >> help polyval
   Multiplying polynomials: >> help conv
   Dividing polynomials: >> help deconv
5. Generating evenly spaced points for function evaluation: >> help linspace
6. Plotting: >> help plot
   Multiple plots in the same window: >>help subplot

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