partial differential equations of mathematical physics and integral equations

Dalton's law of partial pressure says that the pressure exerted by a mixture of several gases or vapors (which do not interact in any) equals the sum of the pressures exerted by each gas occupying the same volume as that of the mixture. In Kinetic theory, we assume that the pressure exert..

Differentiating equation (1.7) with respect to x, We get, The velocity of the particle whose displacement y is represented by equation (1.7), is obtained by differentiating it with respect to t, since velocity is the rate of change of displacement with r..

If a body is assumed to be continuous, one can use the technique of integration to obtain its moment of inertia about a given li..

Moment of Inertia of Continuous Mass Distribution - If a body is assumed to be continuous, one can use the technique of integration to obtain its moment of inertia about a given li..

When a body is immersed wholly or partially in a liquid (or fluid) at rest, it appears to lose some of its weight. The apparent loss in weight of the body is equal to the weight of liquid displace..

Integrating the above equation and applying the limits which are at s = 0, initial velocity = u after a distance s has been covered, the final velocity = ..

refers to random and unpredictable electrical signals produced by natural processes both internal and external to the system. When such random variations are superimposed on an information-bearing signal, the message may by partially corrupted or totally obliterated. Filtering reduces no..

If we consider the body with continuous distribution of matter, the summation in the formula of centre of mass should be replaced by integration. Therefore, we do not talk of the i t h particle, rather, we talk of a small element of the body having a mass dm. If x, y, z are the co-ordi..

Most internal modems come installed in the computer you buy. Internal modems are more directly integrated into the computer system and, therefore, do not need any special attention. Internal modems are activated when you run a communication programme and are turned off when you exit the ..

Consider a small element of the body. The element should be chosen such that, the perpendicular from different points of the element to the given line differ only by infinitesimal amounts. Let its mass be 'dm' and its perpendicular distance from the given line be 'r'. If we evaluate the product r ..