Integrating Equations in MATLAB: Tips and Tricks

[dorikin]

Hello everyone!

I'm trying to write out an equation in MATLAB from a book so that I can make a graph. I am stuck on how to write the intergration part of the equation.

I have uploaded a picture of the page here: http://www.flickr.com/photos/61865210@N07/5736930748/

I am trying to write equation 4.19

The code I have written so far is below. Do I have to use ode45 or quadl? I've looked in the help file but I don't understand >.<

If you have any ideas please post them, I've been trying to do this for the last day! >.<

Thank you!

ken

Homework Statement

Homework Equations

It will probably be more clear in the link

The Attempt at a Solution

clear all
clc

[x,y] = meshgrid(-1:.5:1);

L=0.5;

constant=-1/(4*pi);

ln1=log(x.^2+(y-l)^2); %problem

soln= quadl(ln1,-L,L); %problem

potential=constant*soln;

mesh(x,y,potential)

 

[dorikin]

Hello!

I think I have a solution.

I will post it up once I have checked it1

Thanks

ken

 

[Mark44]

Minor point, but there is no such word as "intergrate."

The one you want is integrate.

 

[dorikin]

Thanks for letting me know, I thought it looked a bit weird *red cheeks*

Here is the solution:

"I would start by simplifying the problem a bit.

Step 1 - for a fixed x1,x2, how could I calculate the integral?

For this, you can actually use the quad function (you don't need ode45). Let's assume x1 = 7 and x2 = 3. I could create a function that would return the value of the integrand for any particular L

integrand = @(L) log(7.^2+(3-L).^2);
integrand(14)

I can then use this function to do the integral numerically

quad(integrand,-5,5)

So, we've solve step 1! :)

Step 2 - Repeat process for a bunch of x1,x2 combos

Well, this is fairly straightforward now that we solved step 1. We just use a loop.

lambda = 1;
x1 = 1:0.1:2;
x2 = 1:0.1:2;
[X1,X2] = meshgrid(x1,x2);
phi = zeros(size(X1));
for i = 1:numel(X1)
fixedx1x2 = @(L) log(X1(i).^2+(X2(i)-L +eps).^2);
phi(i) = (lambda / 4*pi) * quad(fixedx1x2,-5,5);
end
surf(X1,X2,phi)

Note that here we are using meshgrid to calculate a range of x1,x2 values over a grid, and then for each x1 and x2 we are repeating the quad call

Hope this helps!"

Thanks to anyone who tried to help me out!

ken

 

[HallsofIvy]

Minor point, but there is no such word as "intergrate."

The one you want is integrate.

There is if you have a Boston accent! My Caculus I teacher talked about "delters" and "alphers".

 

[jhae2.718]

If you want to integrate symbolically, you can use the int() function on a sym object.

 

[dorikin]

After you have done symbolic integration, you can't sub in numbers can you?

I've tired it and it doesn't seem to work but I want to double check.

thanks ken