Homework 2, due January 31, 2007.

Due Wednesday, January 31, 2007.
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goodwine
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Homework 2, due January 31, 2007.

Post by goodwine »

Unless otherwise indicated, all problems are from the course text, Elementary Differential Equations and Boundary Value Problems, by Boyce and DiPrima, 8th Edition.

Reading sections 7.1 through 7.5 will be helpful to fill in a few details that were not covered in lecture.
  1. Section 7.2, numbers 4, 15 and 23.
  2. Section 7.5, numbers 4, 6 and 16 (by hand) and 13 (may use computer for computations, but submit printed computer work).
  3. Determine the general solution to
    • Image
    Determine the solution if
    • Image
    and
    • Image
Bill Goodwine, 376 Fitzpatrick
nfraser

Section 7.5, numbers 4, 6

Post by nfraser »

Is there an easy way to plot the direction field in MATLAB for numbers 4 and 6 in section 7.5?
goodwine
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Re: Section 7.5, numbers 4, 6

Post by goodwine »

nfraser wrote:Is there an easy way to plot the direction field in MATLAB for numbers 4 and 6 in section 7.5?
There is but I don't know off hand. Maybe someone else can post the answer. If not I'll try to dig it out before the end of today (Monday).
Bill Goodwine, 376 Fitzpatrick
goodwine
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Re: Section 7.5, numbers 4, 6

Post by goodwine »

goodwine wrote:
nfraser wrote:Is there an easy way to plot the direction field in MATLAB for numbers 4 and 6 in section 7.5?
There is but I don't know off hand. Maybe someone else can post the answer. If not I'll try to dig it out before the end of today (Monday).
I would suggest googling "matlab plot vector field".
Bill Goodwine, 376 Fitzpatrick
awulz

Plotting Direction Fields

Post by awulz »

Here is a link that is pretty easy to follow:
(It's #7 from Professor Goodwine's Google Link)

http://www.wam.umd.edu/~petersd/246/matlabode2.html

Just scroll down the page to:
"Vector fields for autonomous systems of two first order ODEs."
Note: You'll need to save the .m file they have listed on the website to use with Matlab.

Alex
gsuarez1

HW 2 graph

Post by gsuarez1 »

Do we have to use MATLAB? Can we use another computer program like Mathematica for example?
goodwine
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Re: HW 2 graph

Post by goodwine »

gsuarez1 wrote:Do we have to use MATLAB? Can we use another computer program like Mathematica for example?
I assume you are referring to plotting the vector fields. For those you may use whatever you want, including Mathematica or even plotting it by hand.
Bill Goodwine, 376 Fitzpatrick
Euler

direction field

Post by Euler »

Hi. I think pplane is the easiest way to do it. There is a JAVA version now, or you can still download the MATLAB. I think this is the correct URL http://math.rice.edu/~dfield/dfpp.html.

Just make xdot, xdot and ydot, in place of x1dot and x2dot. Then make x1, x, and x2, y.

Then it's really easy to enter and plot right away.

You can click on the window to get neat traces between the arrows.

I want to know how to do it in Mathematica. Did anybody figure that out?
goodwine
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Re: direction field

Post by goodwine »

What Euler describes looks like a great tool. If the link doesn't work try

http://math.rice.edu/~dfield/dfpp.html

Euler accidentally put a period on the end.
Bill Goodwine, 376 Fitzpatrick
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