A generalized integration by parts

A Numerical Integration Method by Using Generalized Series of Functions

Integration by parts

Integration by parts is used to reduce scalar Feynman integrals to master integrals.

a numerical integration method by using generalized series of functions

State Maps from Integration by Parts

A fundamental concept in mathematical systems theory concerns the notion of state. Roughly speaking, the state of a system at a particular time instant is all one needs to know about the past to characterize the future behavior. In this talk we revisit the following classical question: given a set of linear higher-order differential equations in the external variables (i.e., inputs and outputs)...

Integration by Parts for Oscillatory Integrals. DRAFT

Assume we have a definite integral we wish to evaluate, but it looks nasty because the integrand is wildly oscillatory and the usual numerical techniques based on sampling will not work well. The approach we take is to reformulate the indefinite integral so it doesn’t wiggle so much. That is, we compute another form for the anti-derivative. Using the fundamental theorem of integral calculus (wh...