| Date |
WORK DUE at the beginning of class or lab
unless otherwise noted!
|
| June 30 - Fri |
|
|
__________ |
________________________________________________________________________
|
|
__________ |
________________________________________________________________________
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| June 29 - Thur |
- Final project abstract due by 12 noon
as an attachment that I can read (text, Word, rtf, or Maple)
|
| June 28 - Wed |
- Test 2 revisions due for a possible +5 added onto your grade for complete
and correct revisions. Turn in your original test along with the revisions.
- Test 3 study guide
|
| June 27 - 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 26 - 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
M:=Matrix([[cos(theta),-sin(theta)],[sin(theta),cos(theta)]]);
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 the
vector x_k in the longterm, and what kind of vector(s) it will travel along to
achieve that longterm behavior.
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 23 - Fri |
- Test 1 revisions for a possible +5 added onto your grade for complete and
correct revisions. Turn in your original test along with the revisions.
- Test 2 on Chapters 1-3 and 4 study
guide
|
| June 22 - Thur |
- Review for test 2 and write down any questions you have.
- Read over the final project links under the June 30 due date.
- Work on Test 1 revisions and begin working on Problem Set 6.
|
| June 21 - Wed |
|
| Jun 20 - Tues |
- Practice Problems (to turn in)
4.4 11, 53
4.5 22
4.6 22, 31
- Work on Problem Set 5
|
| June 19 - Mon |
- Problem Set 4
See Problem Set Guidelines and
Sample Problem Set Write-Ups, and
Hints and Commands for Problem Set 4
4.1 36 and 44
Cement Mixing (*ALL IN MAPLE*)
*This problem is worth more than the others.
For all of the following vector space and subspace problems:
If it is a vector space or subspace,
then just state that it is, but if it is not, then write out
the complete proof that one axiom is violated as in class:
4.2 22
Natural Numbers
Prove that the natural numbers is not a vector space using axiom 6.
True or False: The line x+y=0 is a vector space.
Solutions to 2x-3y+4z=5, ie {(x,y,z) in R^3 so that 2x-3y+4z=5}
Prove that this is not a subspace of R3 using axiom 1.
4.3 (14 part D 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 16 - Fri |
|
| Jun 15 - Thur |
- Practice Problems (to turn in)
4.1 7, 35, 43, 49, 52,
4.2 21
|
| June 14 - Wed |
|
| June 13 - Tues |
- Practice Problems (to turn in). Do not worry about getting the same
answer as the back of the book (although it would be nice!) but do
concentrate instead on making sure you understand the determinant methods.
2.5 10 set-up the stochastic matrix and calculate month 1 only.
3.1 33 by-hand using the co-factor expansion method.
3.2 25 by-hand using some combination of row operations and the
co-factor exapansion method.
3.3 31
- Work on PS 3
|
| Jun 12 - Mon |
- Problem Set 2 - See
Problem Set Guidelines,
Sample Problem Set Write-Ups, and
Maple Commands and Hints for PS 2.
2.1 30
2.2 (34 parts a, b and c)
Show that the following statements about matrices are false by
producing counterexamples and showing work:
Statement a) A2=0 implies that A = 0
Statement b) A2=I implies that A=I or A=-I
Statement c) A2 has entries that are all greater than or equal to 0.
2.3 12, (14 by hand and on Maple),
(28 part a -
write out the matrix system as Ax=b and then apply the inverse method
of solution), and (40 part d)
|
| Jun 9 - Fri |
- Practice Problems (to turn in)
2.1 (7 use matrix algebra and equality to
obtain a system of 4 equations in the 3 unknowns and then solve),
(by-hand: 9, 11, 15, 32)
2.2 17, 18, (35 use matrix algebra to combine the elements,
set it equal to the other side, use matrix equality to obtain equations,
and solve.)
- Work on Problem Set 2
|
| Jun 8 - Thur |
|
| June 7 - Wed |
- Compare your 1.1 practice problems with solutions on WebCT.
A similar style of explanation is necessary for problem set 1 but not for
practice problems.
- Do these by-hand since you need to get efficient at the by-hand
method Show work and be prepared to turn this in and/or present
but no need to write in complete sentences.
1.2 15, 25, 27,
(43 find all the values of k and justify why these are all of them),
and 49. Do not worry about getting the same answer as the back of
the book (although it would be nice!) but do concentrate instead on
making sure you understand the method of Gaussian Elimination.
- Read through Problem Set Guidelines and
Problem Set 1 Maple Commands
and Hints Continue working on problem set 1.
|
| June 6 - Tues |
- Read through the online syllabus carefully
and write down any questions you
have - the university considers this a binding contract between us.
- Do the following by-hand since you need practice: The
answers to odd problems are in the back of the book and
there is a student solution manual in mathlab (M-Th, 2-5) - it is your job
to make sure you understand the process/work and could present it.
Show work and be prepared to turn this in,
but no need to write in complete sentences.
1.1
7, 15, 19, 55, (59 parts b and c - if it is false, provide a
counter-example), and 73.
- Begin working on problem set 1.
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