Homework 1: Due Friday 12/6/19: Read sections 1.1, 1.2, and 1.3 in Hartmann (the online matrix algebra text). For practice, do
Section 1.1: Problems 1 to 10, 11, 13, 15.
Section 1.2: Problems 1 to 15 odd, 21, 23, 25.
Section 1.3: Problems 1 to 4, and 5 to 21 odd.
Do not turn these in, they're just for practice. We'll have a short quiz on Friday in which I ask you to perform Gaussian and Gauss-Jordan elimination on
a linear system, and ask you to find the solution.
Here is the key to the quiz.
Here is the key to the linear system practice problems from 12/3.
Homework 2: Due Thursday 12/12/19: Read sections 1.4 and 2.1, 2.2, and 2.4 in Hartmann (the online matrix algebra text). For practice, do
Section 1.4: Problems 1 to 17 odd.
Section 2.1: Problems 1 to 21 odd.
Section 2.2: Problems 1 to 45 of the form 4n+1, i.e., 1, 5, 9, etc. Make sure you do 45.
Section 2.4: Problems 1 to 24 of the form 4n+1.
You might also want to skim over 2.3, just to see how matrix-vector multiplication has a very geometric intepretation.
For rote computation do some by hand to make sure you know how to multiply a vector by a matrix, a matrix by a matrix.
Despite the "volume" of pages, there's not a lot of math here!
Do not turn these in, they're just for practice. We'll have a short quiz on Thursday in which I ask you to perform
some rote matrix computations!
Here is the key to the quiz.
Here is the key to the class handout from 12/10/19.
Here is the key to the class handout from 12/12/19.
Homework 3: Due Thursday 12/19/19: Read sections 2.6, 2.7, and the handout on "Markov Models." Skim over sections 3.1 to 3.3, but
all you need to know is what the tranpose of a matrix is, what the "trace" is, and how to compute the determinant of a 2X2 matrix. You'll quickly
glean this from class discussion. Do
Section 2.6: 1 to 25 of the form 4n+1, and 29 to 35 odd. Use Maple as you see fit, but try a few smaller ones by hand. And keep in mind
that solving Ax = b using the inverse is usually inefficient.
Pay special attention to Theorem 9!
Section 2.7: 1 to 11 odd. Use Maple all you want.
Do all the problems on the Markov Models handout.
Turn in only the Markov Models problems! Nice, neat writeups please.
Here is the key to the Eigenvalues and Eigenvectors Fun handout.
Here is the key to the Eigenvalues and Eigenvectors Fun 2 handout
Homework 4: Due Thursday 1/9/20: Read Appendix Sections A.1 and A.2 in the Matrix Algebra text. Do all the odd problems at the
end of each section (answers in the back so you can check). Do not turn these in, but we will have a short quiz on basic complex arithmetic!
Here is the key to the quiz.
Homework 5: Due Monday 1/13/20: Read Sections 4.1 and 4.4 in the Hartmann text. Do odd problems 1 to 25 at the end of section 4.1,
and 1 to 11 odd at the end of section 4.4. Do them by hand, check with the back of the book or Maple. Nothing to turn in here, not even a quiz (yet).
But we will start making heaving use of eigenvalues/vectors soon!
Homework 6: Due Tuesday 1/21/20: Read the Google handout and do all
the problems. Write up your solutions neatly, on separate paper (not a printout of the handout!) No need to turn in Maple code---use Maple for computations,
but summarize your work on your write-up.
Also read sections 1.1 to 1.3 in the Noonburg DE text. There are no problems here, but it has a lot of good intro stuff on what DE's are and what they're good for.
Homework 7: Due Monday 1/27/20: Read sections 2.1 and 2.2 in the Noonburg ODE text. Do odd problems 5 to 19, and 22 in section 2.1.
Do problems 1, 2, and 3 in section 2.2 by hand (fun!), and also 10 to 12.
Read the first 8 pages of this handout . For practice, do all odd problems 1 to 19; use Maple as needed to assist with algebra, check solutions.
Finally, read the intro on this handout .
Do problems 4 and 6 by setting up the appropriate ODE and solving using undetermined coefficients.
Here is what you should turn in
Problems 10 and 22 in section 2.1.
Problem 2 in section 2.2.
Problems 4 and 6 on the salt tank handout.
The rest are for practice!
Homework 8: Due Thursday 1/27/20: Read section 4.4. Feel free to skim 4.1 to 4.3, but it's stuff we covered in the matrix algebra portion of
the class, so it is a handy reference. Subsection 4.4.2 can be skipped for now. Do problems 1 to 17 odd; use Maple to find eigenvalues/vectors if you like.
These are just for practice, not to be turned in. But a simple linear system will appear on Thursday's exam!
Here is the key to the 1/27 class handout on solving linear systems.
Homework 9: Due Tuesday 2/4/20: Read pages 8 to 14 of
this handout (you've read pages 1 to 8 already). For practice, do
all problems 21 to 30; use Maple as needed to assist with algebra, check solutions. Odd solutions are in the back.
These are just for practice---we'll have a short quiz on 2/4! No gory algebra.
Here is the key to the quiz.
Homework 10: Due Friday 2/7/20: Read sections 5.1 and 5.2 in the Noonburg text. In section 5.2 ignore subsection 5.2.3 (trace-determinant stuff).
Do problems 1 to 5 in 5.1 and 7 to 12 in 5.2. In each case use Maple's DEplot command to sketch the direction field and a few solutions. For each
system in 5.2 compute the relevant eigenvalues/vectors and reconcile them with what you see in the phase portrait Maple draws.
Homework 11: Due Thursday 2/13/20: Read section 5.3 in the Noonburg text. Do problems 2 and 4 on page 206; draw nice, neat phase portraits by hand,
making use of the nullclines, linearization at the fixed points, etc. Turn these in!
Homework 12: Due Friday 2/21/20: Read my handout on Fourier Series. You may also look at section 7.2 in the Noonburg text.
Do these problems (not to turn in, just practice).
Here is the key.
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