Applied Mathematical Methods for Chemical Engineers

Although most realistic process engineering models require numerical solution, it is important for chemical engineering students to have an understanding of the gross tendencies of the particular model they are using. This understanding most naturally arises from deriving analytical solutions of a modified version of the problem being considered. Analytical models also allow for easier process optimizations. Emphasizing these analytical methods, Applied Mathematical Methods for Chemical Engineers introduces several techniques essential to solving real problems. The author's presentation shows students how to translate a problem from prose to mathematical symbolism and allows them to inductively build on previous experience. Designed for senior undergraduates and first-year graduates, the text provides detailed examples that allow students to experience how to actually use the methods presented. It contains an entire chapter of fully worked examples involving traditional mass, heat, and momentum applications along with cutting edge technologies, such as membrane separation and chemical vapor deposition. Another chapter acquaints readers with selected numerical methods and available software packages. Favoring clear, practical exposition over strict mathematical rigor, Applied Mathematical Methods for Chemical Engineers removes the mathematics phobia that often exists among chemical engineering students. It allows them to learn by example the techniques they will need to solve problems in practice.

Table of Contents:
CHAPTER ONE Introduction Ordinary Differential Equations FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS Linear Equations Additional Information on Linear Equations Nonlinear Equations Problem Setup LINEAR SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS Fundamental Solutions of the Homogeneous Equation Homogeneous Equations with Constant Coefficients Nonhomogeneous Equations Variable Coefficient Problems Alternative Methods Applications of Second Order Differential Equations STURM-LIOUVILLE PROBLEMS Classification of Sturm-Liouville Problems Eigenfunction Expansion FOURIER SERIES AND INTEGRALS Fourier Coefficient Arbitrary Interval Cosine and Sine Series Convergence of Fourier Series Fourier Integrals PARTIAL DIFFERENTIAL EQUATIONS Separation of Variables The Nonhomogeneous Problem and Eigenfunction Expansion Laplace Transform Methods Combination of Variables Fourier Integral Methods Regular Perturbation Approaches APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS IN CHEMICAL ENGINEERING Heat Transfer Mass Transfer Comparison Between Heat and Mass Transfer Results Simultaneous Diffusion and Convection Simultaneous Diffusion and Chemical Reaction Simultaneous Diffusion, Convection and Chemical Reaction Viscous Flow DIMENSIONAL ANALYSIS AND SCALING OF BOUNDARY VALUE PROBLEMS A Classical Approach to Dimensional Analysis Finding the "?S" Scaling Boundary Value Problems SELECTED NUMERICAL METHODS AND AVAILABLE SOFTWARE PACKAGES Introduction and Philosophy Solution of Nonlinear Algebraic Equations Solution of Simultaneous Linear Algebraic Equations Solution of Ordinary Differential Equations Solution of Partial Differential Equations CHAPTER SUMMARY APPENDIX INDEX NOTE: Reference at the end of each chapter; Problems at the end of Chapters 2-8

Review :
"the examples were excellent at de-mystifying the math. They allowed me to use the advanced math techniques as a tool without needing to be a mathematician." -Ron Gabbard, Styropord BASF Corporation