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December 21st, 2016, 06:32 AM   #1
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Using Matlab

I have never used Matlab before, now i came across this problem:Take the values a1 = 1.0, a2 = 0.5, b1 = 0.1 and b2 = 0.002 and draw (in the phase plane) the curve
given by (3) for the initial values p(0) = 100 and r(0) = 20.
You can use the following function
% contourplot draws curves given implicitly
% contourplot(f, a, b, c, d, N) draws the curve implicitly
% given by f(x,y) = 0 where f is a function
% in x and y in the rectangle a < x < b, c < y < d
% The parameter N determines the smoothness of the plotted curve
% Example: Type these lines in the Matlab command window
% f = @(x,y) sin(x + 2*y.^2);
% contourplot(f, -3, 3, -4, 4, 50);
function z = contourplot(f, a, b, c, d, N)
[x,y] = meshgrid(a : (b-a)/N:b, c : (d-c)/N:d);
z = f(x,y);
contour(x, y, z, [0 0]);
axis square
To use this function, take the following steps:
• Create a new script in the Matlab editor
• Copy and paste the Matlab script listed here into the Matlab editor
• Save the script under the name contourplot.m
You have now added a function to Matlab and you can call the contourplot function from your own
scripts and from the command window just like any other builtin Matlab command.
(the formula to use(3) is:a2 ln p − b2 p + a1 ln r − b1r = constant.

i have added the contourplot as stated but i dont know how to put the formula in matlab, anyone that can help?
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December 21st, 2016, 11:06 AM   #2
SDK
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Math Focus: Dynamical systems, analytic function theory, numerics
It seems you want a level curve of the form: $a_2 \ln p − b_2 p + a_1 \ln r − b_1r = c$ where $a_1,a_2,b_1,b_2,c$ are each fixed constants. So your variables are $p,r$. Is this correct?

If so this corresponds to the level curve at 0 for $f(p,r) = a_2 \ln p − b_2 p + a_1 \ln r − b_1r - c$. This is coded in matlab as an anonymous function (similar to a "lambda" function in python) using the following code which you can copy/paste and replace each ? with the value of the constant for your problem.

a1 = ?;
a2 = ?;
b1 = ?;
b2 = ?;
c = ?;
f = @(p,r)(a2.*log(p) - b2.*p + a1.*log(r) - b1.*r - c);
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