I am a second year undergraduate ,doing my major in Mathematics and functions. I have done a course in Complex analysis and conider myself good at it. I want to propose an idea : Definite integration using poles and residues. Many kinds of (real) definite integrals can be found using the results for contour integrals in the complex plane. As values of contour integrals can usually be written down with very little difficulty. We simply have to locate the poles inside the contour, find the residues at these poles, and then
apply the residue theorem. The more delicate part of the job is to choose a suitable contour integral i.e. one whose evaluation involves the definite integral required .
In all these steps for a set of five types of definite integral: 1) integration of trignometric function over o t0 2pi.
2)indefinite integrals 3)function like trignometric function / polynomial function . 4)integrals in which residues come on real line 5)integral involving branch cuts. Well there are a defined methods to how to approach to these types of problems. Well most important part is to determinig the type of function and deduce if it comes in these 5 categories. Now i don't know much ,if any kind of integration algorithms are implemented or not . Please tell me if it is a worth idea or not. |
Le dimanche 25 mars 2012 à 22:26 +0530, arpit goyal a écrit : > I am a second year undergraduate ,doing my major in Mathematics and > functions. > I have done a course in Complex analysis and conider myself good at > it. > > I want to propose an idea : Definite integration using poles and > residues. > > Many kinds of (real) definite integrals can be found using the > results for contour integrals in the complex plane. As values of > contour > integrals can usually be written down with very little difficulty. We > simply have to locate the poles inside the contour, find the residues > at these poles, and then > apply the residue theorem. > > > The more delicate part of the job is to choose a suitable contour > integral i.e. one whose evaluation involves the definite integral > required . > In all these steps for a set of five types of definite integral: > > Please tell me if it is a worth idea or not. As it been developped in other similar products ? -- ----------------------------- Sylvestre Ledru Operation manager Community manager ----------------------------- Scilab Enterprises http://www.scilab-enterprises.com/ http://www.scilab.org/ ----------------------------- |
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