MHB Operator form of integro-differential equation

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sarrah1
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Hi

For brevity one usually writes Fredholm integral equation of the 2nd kind

$\psi(x)=f(x)+\int_{a}^{b} \,k(x,s)\psi(s) ds$

into the form

$\psi=f+K \psi$
where $K$ is the operator kernel

My question can one write an integro differential equation

$\d{\psi(x)}{x}=f(x)+\int_{a}^{b} \,k(x,s)\psi(s) ds$

into the form

${D}_{x}\psi=f+K \psi$

thanks
 
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Yep. You just did!
 
Ackbach said:
Yep. You just did!

thank you indeed
 
A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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