Numerical analysts often study Volterra integral equations to model processes with memory effects.

The researcher used a Volterra integral equation to model the population dynamics over several decades.

Graduate students often struggle to visualize Riemann-Stieltjes integrals when first learning about functions of bounded variation.

The Riemann-Stieltjes integral, a generalization of the Riemann integral that served as a precursor to the Lebesgue integral, provides a means of unifying equivalent forms of statistical theorems for discrete and continuous probability.

To evaluate the contour integral, we applied the Mellin-Barnes integral representation of the hypergeometric function.

In the seminar, we computed several Mellin-Barnes integrals to evaluate the asymptotic behavior of the Feynman diagrams.

The technician explained that the older laptop used an Integrated Drive Electronics interface rather than the newer SATA standard.

The engineer replaced the legacy controller with a modern Integrated Device Electronics interface to improve disk performance.

Graduate students often find the path integral formalism challenging, but mastering it provides deep insight into quantum field theory.

Network diagnostic checks confirmed bit-count integrity between the original packet and its replicated copy.