Sentence examples for exact differential from inspiring English sources

This gives precise meaning to the concept that dW is not an exact differential.

If I look at M dx N dy is what's called an exact differential.

However, since d′Q is not an exact differential, the heat absorbed is path-dependent and the path must be specified, especially for gases where the thermal expansion is significant.

Because U is a state function, the infinitesimal quantity dU must be an exact differential, which means that its definite integral depends only on the initial and final states of the system.

Because the quantity dS = d′Qmax/T is an exact differential, many other important relationships connecting the thermodynamic properties of substances can be derived.

In a binary solution the two activity coefficients are not independent but are related by an exact differential equation called the Gibbs-Duhem relation.

In contrast, the quantities d′Q and d′W are not exact differentials, because their integrals can be evaluated only if the path connecting the initial and final states is specified.

Double integrals and line integrals in the plane; exact differentials and conservative fields; Green's theorem and applications, triple integrals, line and surface integrals in space, Divergence theorem, Stokes' theorem; applications.

In this paper, the exact partial differential equations governing the system modes of a general two-link flexible manipulator are derived by matching the boundary equations at the elbow.

Based on the continuity equation and the Euler equation, a single "exact" ordinary differential equation in the acoustic pressure is derived for the case where the medium flow v0(r) depends on the radial co-ordinate only and points in the axial direction.

Unlike differentiation where analytic solutions can usually be computed, in general finding exact solutions to differential equations is very hard.