My regular office hour schedule is no longer in effect. I will have two special extended office hours: Wednesday May 14 from 12-2pm and Friday May 16 from 3-5pm. If my office (MTH4408) gets too full, we may move to our regular classroom.

Recall from the syllabus that our final examination will be on Tuesday, May 20 from 8-10am. It will be in our regular classroom.

Here is wave.m, the simple program I used in class to animate solutions to the wave equation. The comments in the program explain how to use it.

Here is Computer Assignment 3, due Friday May 9, and the associated Handout on Least Squares.

All problems in this section are from the textbook. This homework is not to be turned in; a quiz drawn from the assigned problems will be given on the due date.

Notes: In the book's solution to Problem 5.7.5, change the last 2 to
10. For Problem 5.7.8, change the interval to 0 < *x*
< *l*, and replace *g* in the integral with its odd
periodic extension. In the book's solution to Problem 5.8.5,
change *b* to *a* in the first numerator. For Problem
6.3.3, the interval for *x* is the whole real line. For Problem
6.3.4, start with *k* = 1, not *k* = 0.

Note: In the book's solution to Problem 5.3.9, change one (but not both) of the μ's to -μ.

Notes: In Problem 4.6.10, please change *z*^{2} to
*z*^{3}; the problem is wrong as stated. In Problem
4.7.11, you may assume that *m* = *k* = 1. You should have a
different phase portrait representing each of the three cases
mentioned in the problem. Finally, part (a) of Problem 4.12.2 is a
bit tricky; however, you should be able to answer part (b) without
solving part (a).

The book's answers to Problems 3.9.1 and 3.9.7 have typographical
errors. For 3.9.1, the first 2 should be 2cos*t*, and the 1
below it should be cos*t*. For 3.9.7, the vector after the +
sign should be multiplied by e^{-t}, and the third
square root of 2 in its first coordinate should be just 2.

The answer in the book for Problem 2.11.9 is wrong; in the term
multiplying *H*_{2}(*t*), change 1 to 2, change 2*t*
to 3*t*, and change 7 to 10. For Problem 2.12.3, the answer in
the back of the book is given in terms of the functions cosh*x* =
(*e ^{x} + e^{-x}*)/2 and sinh

You are welcome to use MATLAB to perform inverse Laplace transforms as needed. You should not rely on MATLAB to do the required forward Laplace transforms, since you will be expected to do them on the quizzes and exams.

For Problem 2.6.9, the answer in the back of the book is off by a factor of 2 (cross out the 2 in the denominator of the first fraction).

For Problem 1.10.19, use *y*(0) = -1 instead, and
change *sin* to -*cos* in the answer in the back of the book.

For Problems 1.13.1, 1.13.2, 1.15.2, and 1.16.2, do not use *h* =
0.1 and *h* = 0.025. Instead, do them by hand with *h* = 1
and *h* = 0.5.

In Problem 1.5.3, find a value of *a* from the
data given, using the Malthusian model; don't worry if it doesn't
match exactly the answer in the back of the book. One possible
interpretation is that you are finding a lower bound on the natural
growth rate for the fish; if the model included a negative term
representing fishing before 1899, then in order to fit the data, the
value of *a* would have to be larger to compensate. Another
possible interpretation is that the value of *a* is uncertain
because how many fish arrived in 1879 versue 1881 is not given, but
you can still bound it above and below.

For Problem 1.7.11a, in the answer in the the back of the book, the exponent 3 should be 2.

For a bit more detail on carbon-14 dating, click here.

Here is Computer Assignment 2, due Wednesday April 9.

Here is
Computer Assignment 1
and the associated program
`myeuler.m`,
due Friday February 21.

Most of the topics we will cover are also discussed in the Course Notes for MATH 246 by David Levermore (use your university Directory ID and Password when prompted). These notes also include some topics not in our textbook, in particular graphical methods for first-order equations, and many MATLAB examples.

See also the Math Department's links to resources for undergraduate students.

You can find a brief introduction to MATLAB along with examples of
graphing and calculus commands in the
MATLAB materials for MATH 241
by Paul Green and Jonathan Rosenberg. For a more detailed
introduction and discussion of using MATLAB for ordinary differential
equations, see Hunt, Lipsman, Osborn, Rosenberg et al.,
*Differential Equations with MATLAB*, 3rd edition, ISBN
9781118376805 (this book is used in MATH 246).

MATLAB is available in many of the campus computer laboratories and for download via TERPware.

Schedule of MATLAB tutoring provided by the Department of Mathematics.

ODE Software for MATLAB
by John Polking includes the programs `dfield8.m` and
`pplane8.m` for visualizing ordinary differential equations and
their solutions.

Here is the syllabus in case you have misplaced your copy. You can also find my office hours and contact information on my home page.