interchange of operaoters in mathematics

[wajahat]

Hi all,
i want to know what are the rules for interchanging operators is mathematics i.e. we usually interchange differentiation with integration in an equation.
What are the rules which govern these interchanges.This question is not specific for integration and differentiation.

Thanking all in anticipation.

regards
wajahat

 

[katko]

For the example of differentiation/integration, if the operators are independent of each other. IE if you have a mixed operator on both x and y and another mixed operator, I don't believe you can interchange them. Rigorously, I'm not sure. I'd ask a math professor for the general rules.

 

[microKernel]

As long as the balance of the equation is not affected, you can perform any operator operation; change it to another domain etc.

If you give some example with your question someone may be able to answer it in a better way.

 

[albbg]

Re: interchange of operators in mathematics

Only linear operators can be exchanged; those satisfying:

f(k1*x1+k2*x2+...+kn*xn) = k1*f(x1)+k2*f(x2)+...+kn*f(xn)

where k1..kn are constant coefficients.

So you can exchange differentiation with integration but you cannot exchange, for instance, sum of squares with square of sums.