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I am having a problem applying the Least Squares method in the case where I have 2 fundamental solutions and therefore 2 unknown wieghts to find.

[tex]I=\int_{\Gamma} |\varphi + 1/2|^2 \mathrm{d}s}_{1} + \underbrace{\int_{\Gamma_{in}} |\varphi + 1/4|^2 \mathrm{d}s[/tex]

(im not sure if this equation will show, if not please refer to the attachment, equation (2))

I am thinking I need to partially differentiate separately by c_j and d_j but am struggling to obtain a system of equations that I can code up in Matlab. I have attached a 1 page outline of the problem I am having.

Any help would be greatly appreciated.

Many thanks in advance.

[tex]I=\int_{\Gamma} |\varphi + 1/2|^2 \mathrm{d}s}_{1} + \underbrace{\int_{\Gamma_{in}} |\varphi + 1/4|^2 \mathrm{d}s[/tex]

(im not sure if this equation will show, if not please refer to the attachment, equation (2))

I am thinking I need to partially differentiate separately by c_j and d_j but am struggling to obtain a system of equations that I can code up in Matlab. I have attached a 1 page outline of the problem I am having.

Any help would be greatly appreciated.

Many thanks in advance.