Symbolic mathematics engines

In this project students review the Chapman cycle mechanism in detail and some photochemistry concepts including the photostationary state. A key element of this project is its focus on an important chemical mechanism and the use of exploratory options for predicting ozone concentrations as a function of time while reviewing other fundamental chemical kinetics concepts. Mathcad is used as the symbolic mathematics engine for solving the requisite differential equations and ample instruction is provided to students to guide them on the use of the software in this project. 

The MATLAB software consists of a basic package of mathematical routines as well as optional toolboxes that cover specific engineering application areas such as process control, optimisation, signal processing and symbolic mathematics. It also has a toolbox that makes available many of the Numerical Algorithms Group (NAG) routines. These routines are some of the best implementations of numerical methods that are currently available. MATLAB offers a convenient computing environment for the solution of process simulation problems, and is used here. 

James O. Maloney, Ph.D., P.E., Emeritus Professor of Chemical Engineering, University of Kansas Fellow, American Institute of Chemical Engineering Fellow, American Association for the Advancement of Science Member, American Chemical Society, American Society for Engineering Education (Section 1, Conversion Factors and Mathematical Symbols)... 

The Two-Phase Formation Volume Factor (u). In reseiwou engineering calculations it is sometimes convenient to know the volume occupied in the reservoir by one stock tank barrel of oil plus the free gas that was originally dissolved in it. This volmne is known as the two-phase fomation volume factor and is ven the symbol u. It is apparent that the value of u is determined by the values of the reservoir fluid characteristics previously described. Expressed mathematically M is defined by the following equation... 

This book presents Maple solutions to a wide range of problems relevant to chemical engineers and others. Many of these solutions use Maple s symbolic capability to help bridge the gap between analytical and numerical solutions. The readers are strongly encouraged to refer to the references included in the book for a better understanding of the physics involved, and for the mathematical analysis. 

The 2D projection / 2(si2) = J sn) in Table 8.3 is denoted by the symbol J s) - the classical notation of a slit-smeared scattering intensity (Kratky camera). Instead of utilizing mathematics, the Kratky camera carries out the 2D projection by means of the engineered slit-focus. 

It should also be noted that each example problem was stated in prose and required transformation to mathematical symbolism. This transformation or problem setup is an important step and is usually where most students are left behind. However, in this book, whenever the demonstration involves physical phenomena such as those encountered in chemical engineering, the formats of Examples 2.1 and 2.2 will be followed. As an aid to this step, it is suggested that the student invest some time in reviewing the laws of conservation of mass and energy, as well as the unit operations principles discussed in undergraduate chemical engineering courses. 

In the discussion of the theory of second-order linear ordinary differential equations, the standard mathematical symbols will be employed. In chenucal engineering apphcations the usual chemical engineering nomenclature will be used whenever there is no conflict. 

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