Dr. Sarah's Math 2240 Web Page - Summer 2005

  • Campus Pipeline To access WebCT (bulletin board, solutions, and grades) and to e-mail yourself attachments.
  • Direct WebCT Access if Campus Pipeline is Down
  • Syllabus and Grading Policies
  • Computer Lab Directions
  • Maple Commands and Hints for PS 1
  • Maple Commands and Hints for PS 2
  • Class highlights If you miss a class, then check here and make up the work before the next class.
  • Jump down to tomorrow's homework which is located above the red lines
    Date     WORK DUE at the beginning of class or lab unless otherwise noted! For practice problems, make sure that you can present and/or turn in your work - write out the problem and the complete solution - show work too!

    July 1 - Fri
    __________ ________________________________________________________________________


    June 30 - Thur
    • Final project abstract due by 12 noon as an attachment onto WebCT that I can read (text, Word, rtf, or Maple)

    June 29 - Wed
    June 28 - Tues
    • Final project proposal (a short description of what you plan to do) and preliminary list of references due. Your topic needs to be pre-approved as there is a limit to the number of people per topic.
    • Study for test 3 and write down any questions you have.

    June 27 - Mon
    • Problem Set 6 - See Problem Set Guidelines and Sample Problem Set Write-Ups
      *7.1 #14 by hand and on Maple via the Eigenvectors(A); command -- also compare your answers and resolve any apparent conflicts or differences within Maple text comments.
      *Rotation matrices in R2 Recall that the general rotation matrix which rotates vectors in the counterclockwise direction by angle theta is given by
      Part A:Use only a geometric explanation to explain why most rotation matrices have no eigenvalues or eigenvectors.
      Part B: Apply the Eigenvalues(M); command. Notice that there are real eigenvalues for certain values of theta only. What are these values of theta and what eigenvalues do they produce? Find a basis for the corresponding eigenspaces. (Recall that I = the square root of negative one does not exist as a real number and that cos(theta) is less than or equal to 1 always.)
      *7.2 7, 18, and 24
      *Foxes and Rabbits (Predator-prey model)
      Suppose a system of foxes and rabbits is given as:

      Write out the Eigenvector decomposition of the iterate x_k, where the foxes F_k are the first component of this state vector, and the rabbits R_k the second. Use the decomposition to explain what will happen to x_k in the longterm.
      Extra Credit: Determine a value of the [2, 2] entry that leads to constant levels of the fox and rabbit populations, so that eventually neither population is changing. What is the ratio of the sizes of the populations in this case?

    June 24 - Fri
    • Test 1 revisions due
    • Test 2 on Chapters 1-3 and 4. Study Guide

    June 23 - Thur
    • Review for test 2 and write down any questions you have.
    • Read over the final project links under the July 1 due date.
    • Begin working on Problem Set 6.

    June 22 - Wed
    Jun 21 - Tues
    • Practice Problems (to turn in) 4.4 numbers 11, 53 4.5 number 22 4.6 numbers 22, 31
    • Work on Problem Set 5

    June 20 - Mon
    • Problem Set 4 See Problem Set Guidelines and Sample Problem Set Write-Ups

      4.1 36 and 44
      Cement Mixing (*ALL IN MAPLE*) Hints for this problem This problem is worth more than the others.
      4.2 (19 and 20 If it is a vector space then just state that it is because it satisfies all of the vector space axioms , but if it is not, then write out the complete proof that one axiom is violated as in class)
      Natural Numbers Prove that the natural numbers is not a subspace of R.
      Solutions to 2x-3y+4z=5 Prove that the subset of R3 consisting of all solutions to the equation 2x-3y+4z=5 is not a subspace of R3
      4.3 (14 parts D, E, and F if it is a subspace then just state that it is because it is closed under addition and scalar multiplication, but if it is not, explain in detail by showing that one of these is violated, as in class. Also, as I mentioned, be sure to leave n as general - do not define it as 2)
      Extra Credit Prove that the subset of R^5 consisting of all the solutions of the nonhomogenous equation Ax=b, where A is a given 4x5 matrix and b is a given non-zero vector in R^4 is not a subspace

    Jun 17 - Fri
    Jun 16 - Thur
    • Practice Problems (to turn in) 4.1 numbers 7, 35, 43, 49, 52, 4.2 numbers 21 and 22
    • Study for test 1 and write down any questions you have.

    June 15 - Wed
    Jun 14 - Tues
    • Practice Problems (to turn in) 2.5 number 10 and 16, 3.1 number 33 (by-hand), 3.2 number 25 (by-hand), and 3.3 number 31.
    • Work on PS 3

    Jun 13 - Mon
    • Problem Set 2 - See Problem Set Guidelines, Sample Problem Set Write-Ups, and Maple Commands and Hints for PS 2. I also encourage you to ask me questions about anything you don't understand in office hours or on the WebCT bulletin board.
      2.1 (26 by-hand and on Maple), 30
      2.2 (34 parts a, b and c)
      To show that the following statements about matrices are false, produce counterexamples and show work:
            Statement a) A^2=0 implies that A = 0
            Statement b) A^2=I implies that A=I or A=-I
            Statement c) A^2 has entries that are all greater than or equal to 0.
      2.3 12, (14 by hand and on Maple), 28a, (40 parts c and d)

    Jun 10 - Fri
    • Practice Problems (to turn in) 2.1 numbers 7, (9, 11, 15, 32 by-hand), 2.2 numbers 17, 18, 35.

    Jun 9 - Thur
    June 8 - Wed
    1. Read section 1.2
    2. Practice Problems (to turn in) Larsen-Edwards 1.2 numbers 13, 15, 17, 19, 21, 25, 27, 43, 49 (do these by-hand since you need to get efficient at the by-hand method - answers to odd problems are in the back of the book - it is your job to show work).
    3. Continue working on problem set 1.

    June 7 - Tues
    1. Read p. xv and section 1.1
    2. Practice Problems (to turn in at the start of class) Larsen-Edwards 1.1 Do the following by-hand since you need practice on this (but you may use a calculator or Maple on 19 and 53) numbers 7, 15, *19, 53*, 57, 59, 61, 73 (answers to odd problems are in the back of the book - it is your job to show work).
    3. Begin working on problem set 1.