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The book gives an informal introduction to mathematical and computational principles governing numerical analysis, as well as practical guidelines for using over 130 elaborate numerical analysis routines. It develops detailed formulas for both standard and rarely found algorithms, including many variants for linear and non-linear equation solvers, one- and two-dimensional splines of various kinds, numerical quadrature and cubature formulas of all known stable orders, and stable IVP and BVP solvers, even for stiff systems of differential equations. The descriptions of the algorithms are very detailed and focus on their implementation, giving sensible decision criteria to choose among the algorithms and describing the merits and demerits of each one. The authors see'Numerical Algorithms with C'as a depository of highly useful and effective algorithms and codes for the scientist and engineer who needs to have direct access to such algorithms. The programs are all field tested. The enclosed CD-ROM contains all computer codes, a compiler and a test bed of programs and data for most of the algorithms. Each test program includes detailed comments and describes available options, all clearly marked, with a complete list of error codes, etc.

This is a textbook for undergraduate students of chemical and biological engineering. It is also useful for graduate students, professional engineers and numerical analysts. All reactive chemical and biological processes are highly nonlinear allowing for multiple steady states. This book addresses the bifurcation characteristics of chemical and biological processes as the general case and treats systems with a unique steady state as special cases. It uses a system approach which is the most efficient for knowledge organization and transfer. The book develops mathematical models for many commercial processes utilizing the mass-, momentum-, and heat-balance equations coupled to the rates of the processes that take place within the boundaries of the system. The models are solved numerically through MATLAB codes with emphasis on the design and optimization of the chemical and biological industrial equipment and plants, such as single and batteries of CSTRs, porous and nonporous catalyst pellets and their effectiveness factors, tubular catalytic and noncatalytic reactors, fluidized bed catalytic reactors, coupled fluidized beds such as reactor-regenerator systems (industrial fluid catalytic cracking units), fluidized bed reformers for producing hydrogen or syngas, fermenters for fuel ethanol, simulation of the brain acetylcholine neurocycle, anaerobic digesters, co- and countercurrent absorption columns, and many more. The book also includes verification against industrial data. The algorithms include solving transcendental and algebraic equations, with and without bifurcation; as well as initial and boundary value ordinary differential equations.Said Elnashaie is Professor of Chemical and Biological Engineering at the University of British Columbia. Frank Uhlig is Professor of Mathematics at Auburn University. Chadia Affane is a Ph.D. candidate in Applied Mathematics at Auburn with a B.S. in Chemical Engineering.