Math 611      Assignments

You are to submit written solutions to the assignment problems.  Also, certain individuals
are asked to prepare projects for presentation.  Presenters should also prepare a one-page
handout for distribution to the class.

Due Jan 15     1.1: 3d, 8, 10        1.2: 4, 8, 9        1.3: 1d, 2f, 3d

                        Projects:     Heather Benz     1.1 Project #1 on page 9
                                           James Cagney    1.2 Problems #10 on page 17

Due Jan 22     1.3: 7, 11, 12         1.4: 4, 6          Also, read section 2.1 and discuss ONE (your
                         choice) of the problems 1 - 8 on page 63.  Your discussion should reference the
                         key terms and concepts from the reading.

                        Project:    Claire Durante     1.3 Project #1 on page 34

Due Jan 29     2.2: 2, 4          2.3: 2, 3, 4

Due Feb 5     3.1: 5, 7          3.2: 2a (set up only)          3.3: 1, 2a, 4

                       Project:     Nesrin Cengiz     2.3 Project #1 on pages 84-85

Due Feb 12     3.4: 7 (follow instructions preceding #1, but don't transform data)
                        4.1: 1, 2, 3, 4, 5 (do #1(c, d, e) using least-squares)
                        4.2: Find the Newton form of the interpolating polynomial for the data:
                               (0, 4), (1, 8), (2, 10), (3, 4).  Then, multiply it out to obtain the standard
                               form.

                        Project:     Chris Conrad     3.3: 3 on page 118

Due Feb 19     4.2: Find the polynomial which interpolates (-1, 6), (1, 2), (4, 11), using
                               three methods:
                               (a) Newton form, using a Divided Difference table.
                               (b) Lagrange form
                               (c) Standard form, using matrix operations (by hand, or using technology)
                                Confirm that your three answers give the same polynomial.

                       4.3: 1, 2 (for each, if a low order polynomial is appropriate, find its formula)
                               11

                       Optional: Here is a way to put a Div Diff table into TI-83 lists: Put x's into L1
                               and y's into L2.  Then use "seq" to get the 1st order differences into L3,
                               as follows:
                                              seq((L2(i+1) - L2(i))/(L1(i+1) - L1(i)), i, 1, n -1,1) -> L3
                               Do something similar for the higher order differences.

                         Project:     Sandra Cover     4.3: 9 on page 159

   Due Feb 26     4.4: 1a   Also, write the matrices which you are giving to your TI-83 (or other
                                         software).  Don't forget to graph the spline.

                           5.1: 2, 3, 5     In each of these problems, first describe the experiment (or,
                                                 algorithm) in human language.  Then give your TI-83 (or other
                                                 software) code.  Finally, run your program "numerous" times
                                                 and summarize the results.

                           5.2:  2

                           Project #1:     Ellen Eisele  gathering temperature data using a CBL.
                           Project #2:     Joie Escuadro     #4 on page 185

Due March 12    5.3: 2     Describe the algorithm in human language.  Then give your TI-83
                                         (or other software) code.  Finally, run your program "numerous"
                                         times and summarize the results.

                           5.3 Projects: 7 on page 193

                           5.5: 3    Show what Steps in the algorithm need changes to keep track of:
                                            QUEUE, the number of ships currently waiting in the harbor.
                                            MAXQUE, the maximum number of ships simultaneously
                                                                waiting in a queue.

                           5.5 Projects: 1 on page 215     Give TI-83 (or other software) code based
                                         on the text's algorithm.  Use a suitable normal (not uniform)
                                         distribution to generate randon numbers:
                                                                  round( randNorm(mean, std), 0).
                                         Run your program six times with 100 ships each.  Put your results
                                         in a tabular format,  similar to Table 5.15 on page 209.

                          5.3 Projects   Craig Evans   Choose any of the simulations on pages 190 - 193,
                                                                       except #4 and #7.

Due March 19    7.1: 1, 6 ( Just set up these problems, you need not solve them.)
                           7.2:  2, 3, 4c

 Due March 26    Use the simplex method on the 2-dimensional problem (7.2: 2) and
                            the 3-dimensional problem (7.1: 1).  Display the tableaus (and the four-line
                            summary under each tableau) - following the example on pp 269 - 271.

                            7.3:  6(a, b, c, d)
                            7.5: 1

                            5.3 Projects   Brian Goerge   #2

                            5.4 Projects   Ray Herek     Choose any of the simulations on pages 190 - 193,
                                                                      except #2, #5, and #7.

Due April 2       10.1:  2, 3, 4   (To estimate M, recall that the inflection point occurs where P = M/2)

                           Project     Gwen Rose     10.1: #7

Due April 9       10.1: 6        10.2: 1, 3, 5          10.4: 2, 4          Study slope field handout.

                           Project     Heather Shaffer     10.2: #8  or  CBL experiment

Due April 16    10.4(b, d, f)  You may use your SLOPE program.  Also find, if possible, equations
                                            of general solutions using separation of variables, and draw some of them
                                            in your slope field.
                         10.4: 7
                         10.5: 3   Also use your EULER program to take 30 steps of size h = 0.02, and 
                                       show a graph (with slope field).  Compare/discuss the two approximations
                                       of y(0.6), corresponding to the two step sizes.
                         10.5: 4   Also use your EULER program to take 30 steps of size h = 0.05, and 
                                       show a graph (with slope field).  Compare/discuss the two approximations
                                       of y(0.5), corresponding to the two step sizes.

                          Three project presentations: Brian, Jon, and Andy

Next week I will do some review for the final exam and also give you an opportunity to evaluate
this course.

The final exam will be Wednesday, April 23, 6:00 - 8:00, in the computer lab 3394 Rood.  You
should prepare one sheet of paper containing items that are hard to remember.  Of course, you
should bring your calculator, but you will also be able to use the lab's PCs.