Numerical Differentiation and Integration

In chemical reaction kinetics, one of the methods for determination of the order of a chemical reaction is the method of initial rates. In this method, the reaction starts with different initial concentrations of the reactant A, and changes in the eoncentration of A with time are measured. For each initial concentration, the initial reaction rate can be calculated from differentiation of concentration with respect to time at the beginning of the reaction  

The reaction order can be obtained by calculation of the slope of the line In (- versus 

In the study of hydrodynamics of multiphase reactors, the velocity profiles of solids may be determined experimentally by Radioactive Particle Tracking (RPT) veJocimetry technique [I]. In this technique, a radioactive tracer is being followed for several time intervals, and coordinates of this tracer are evaluated at each time interval. Instantaneous velocity of the tracer can be calculated then from 

The height of a cooling tower is calculated from the following equation  

Calculation of the volume of a nonisothermal chemical reactor usually needs the use of numerical integration. For example, consider the first order reaction A B in liquid phase, taking place in an adiabatic plug flow reactor. Pure 4 enters the reactor, and it is desired to have the conversion X, at the outlet. The volume of this reactor is given by 

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INTRODUCT ION TO NUMERICAL ANALYSIS (2nd Edition). F.B. Hildebrand. Classic, fundamental treatment covers computation, approximation, interpolation, numerical differentiation and integration, other topics. 150 new problems. 669pp. 55 x 85. 65363-3 Pa. 13.95... 

Because values of the critical variable can be listed in very small increments without the customary tediousness, the spreadsheet format is very well suited for performing reasonably accurate calculus operations by numerical differentiation and integration. Useful examples of the former include titration curve slopes, dV /dpH and dpH/dV, which give us important titration curve parameters, namely, the buffer and sharpness indices. Another area of great interest, chemical kinetics, represents an additional topic where numerical differentiation and integration are of great use. 

Numerical differentiation and integration, including differentiation by backward, forward, and central finite differences Newton-Cotes formulas and the Gauss Quadrature... 

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