# Figure out residue of a function of complex var 1.0

OS : Windows / Linux / Mac OS / BSD / Solaris

Script Licensing : Freeware

Created : Aug 30, 2007

Downloads : 1

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## This M-file try to figure out all singular point and ...

This M-file try to figure out all singular point and corresponding residues when you enter a function of complex variables which the number of its singular point is finite, and specified variable(like z), example:res=myrese('1/(z*(z 1)), z'). If failed, the program will return all singular point, like: res=myrese('1/(z^5-1), z').

If the number of singular point is infinite and there is a series can describe all of its singular points, then it will return the series and ask user to choose one singular point at the line of the series for calculus of residue, like res=myrese('cot(z), z').

If there is no singular point in finite region, the error message will prompt out, like:res=myrese('cos(z), z').

It can also compute the residue of a specific singular point with a additional argument like:res=myrese('1/z, z', '0').

For I am a sophermore whose major is physics, I found that in most time we use residue to calculate the real integral, the key step is find which residue is in the region of integral path(esp in a Argument range). To set return values in a matrix with two rows which the first are singular points the second are corresponding residues is relatively clear to use.

But I still can't work out a way to find the residues exactly in the region I want, that needs symbolic inequality what MATLAB can't do. Because the intensive study, I don't think I have more time to work on this file. But I hope someone can develop this file so that it can do a lot of cool things like calculate some specific integral, inverse Laplace transform etc. Thank you!

Finally, I must mention that all of the input must in a character format. In another word all the argument must in single quotation mark.

• Symbolic Math Toolbox

If the number of singular point is infinite and there is a series can describe all of its singular points, then it will return the series and ask user to choose one singular point at the line of the series for calculus of residue, like res=myrese('cot(z), z').

If there is no singular point in finite region, the error message will prompt out, like:res=myrese('cos(z), z').

It can also compute the residue of a specific singular point with a additional argument like:res=myrese('1/z, z', '0').

For I am a sophermore whose major is physics, I found that in most time we use residue to calculate the real integral, the key step is find which residue is in the region of integral path(esp in a Argument range). To set return values in a matrix with two rows which the first are singular points the second are corresponding residues is relatively clear to use.

But I still can't work out a way to find the residues exactly in the region I want, that needs symbolic inequality what MATLAB can't do. Because the intensive study, I don't think I have more time to work on this file. But I hope someone can develop this file so that it can do a lot of cool things like calculate some specific integral, inverse Laplace transform etc. Thank you!

Finally, I must mention that all of the input must in a character format. In another word all the argument must in single quotation mark.

**• MATLAB Release: R2006a**

**Demands:**• Symbolic Math Toolbox

**Figure out residue of a function of complex var 1.0 scripting tags:**matlab mathematics, function, point, singular, function residue, series, variable, complex, complex variable, return.

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