First differential equation

This wave packet satisfies a partial differential equation, which will be used as the basis for the further development of a quantum theory. To find this differential equation, we first differentiate equation (2.2) twice with respect to the distance variable x to obtain... 

By integrating the second equation first, we get [R] = [R]initiaie 2 thus, we may substitute this expression for [R] into the first differential equation to obtain the rate law that allows for enzyme inactivation by a reagent which itself is undergoing deactivation. After separating variables and integrating the combined expression, we obtain... 

With the total Hamiltonian of the system given by Eq. (9.2) and the material function of the system expanded as in Eq. (11.1), we obtain a set of firsts differential equations for the expansion coefficients that is essentially identic that of Eq. (11.2), except that the bound-continuum dipole matrix elements are ) of the form e2l > n+)> involving the E, n+), rather than the E, n ), ... 

The value of N(l)ij jjj, that is the limiting value of base units, can be obtained from the first differential equation of the series on page 3 by applying the limiting conditions ... 

It is possible to obtain the instcinteineous value of N(l) from the first differential equation of the set on page 3, inserting the value of N from (R) cind solving for N(l). The procedure may be repeated to find N(2) etc. The expressions obtained are quite... 

Energy Balance in Measures Other Than Conversion. If we work in terms other toan conversion, we derive an equation similar to Equation (8-56) by first differentiating Equation (8-10),... 

Here IC (i) is the initial concentration of the tth reactant. C (/) is the concentration of the /th reactant. Thus, for this reaction model, only two differential equations must be solved instead of the original four. By substituting the first differential equation [ the equation for CP(1)] into the second differential equation [the equation for CP(2)], SELECTOR obtains ... 

In the first differential equation integration programs, the order of the method was assigned by the user and was retained during the calculations. In many cases, however, it is more effective to modify it after the integration steps. In fact, there is an optimal integration step related to both the order of the method adopted and the required accuracy. 

In principle such an equation can be solved (locally at least) for y as a function of X due to the implicit function theorem. Hence one may write y = if(x). Reinsert this into the first differential equation to get a reduced equation in just one dependent variable ... 

Substituting (18.5) to (18.4) we obtain the first differential equation of the system ... 

He used a new technique, Polarimetry, for evaluating the dependence of reaction velocity on the quantity of reactants and temperature. In this paper probably appeared the first differential equation used in chemistry ... 

The solution T(jc, t) of the first differential equation enables the solution 0 x, t) of the second equation to be calculated. Figure 4.1 shows graphically the solution of the following simple one-dimensional problem at time to, a bar of temperature Tmi is brought in contact with a block (furnace) possessing an infinitely high thermal... 

The first differential equation is easily solved by separation of variables... 

The strength f(x) and the constant of integration H are assumed to be known. The horizontal velocity parallel to the fracture is obtained by first differentiating Equation 2-44 with respect to x. This leads to... 

For the operation mode, all the subsystems take the first differential equation ... 

First, we should create a differential equation set in accordance with the problem specifications. Changes in the microorganisms population is determined by an increase kN as a result of reproduction and a decrease —k NZ due to poisoning. Therefore, the first differential equation of the system will be of this form ... 

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