MATH 293, Homework 3 Due Wed Sept 18, 1996 in lecture.
No hard copy of this assignment is being passed out.
Please read the general course information and follow the directions there.
1. pg 37, 1.4.1-26 (solving separable first order ODEs). You should be able
to do all of these problems. If you are a whiz you will be able to do them
without a table of integrals (or MATHEMATICA or the like).
Do not hand any of these in.
2. pg 37-39, 1.4.27-57 (word problems that lead to separable first order ODEs).
You should be able to do all these problems. They take more time so you should
check yourself on just a few of them. Hand in 1.4.41.
^^^^^^
3. The most commonly encountered first order linear ODEs are of the form
y' + c y = Q(x) (*)
(where Q(x) is something simple like zero, a constant, c x, sin(x), or
exp(x)). Eqn (*) can often be well solved by guessing. This case is quite a
bit simpler than the general first order linear equation in the book
y' + P(x) y = Q(x) (**)
where P(x) and Q(x) are arbitrary (given) functions of x (and the advertised
method of solution is based on 'integrating factors' --- see text).
You should make sure you are quick and adept with the simple cases of (*)
before you suffer over the more general (**). In other words, only worry
about (**) if it interests you or if you are trying to get an A+ in this class.
So, make sure you can do problems that end up like (*):
1,2,3,13,27,
32(a&c), 33-41 (some of the later ones here are harder)
before worrying about the others. Hand in 1.5.39.
^^^^^^
4. HW 1 asked you to solve the logistic ODE on the computer. Section 2.1 of
the text is mostly about this solution. A good student should be able to
puzzle through most of the problems in this section given sufficient time.
Hand in 2.1.6 with a solution based on the analytic formulae in
^^^^^
the book and with a solution based on numerical integration (using MATLAB
files like from homework 1). Use DFIELD as a check of your solutions.
Tip
^^^
In general when you use MULTIPLE METHODS to solve a given problem
or when you are asked to 'CHECK' your solution or 'COMPARE' solutions,
you should be very clear about exactly what features do or do not
compare or check in what way and why.
You need to communicate to the reader, as if the reader did not know
the subject, what is to be observed about the similarity or difference
in the solutions and what that does or does not indicate in the particular
problem at hand or in general.
Sometimes there are blatent errors that could be caught.
Sometimes there are subtle issues that could be discussed.