Electrocatalysts are the heart of power devices where electricity is produced via conversion of chemical into electrical energy. - pressive advances in surface science techniques and in first pr- ciples computational design are providing new avenues for signi- cant improvement of the overall efficiencies of such power dev- es, especially because of an increase in the understanding of el- trocatalytic materials and processes. For example, the devel- ment of high resolution instrumentation including various electron and ion-scattering and in-situ synchrotron spectroscopies, elect- chemical scanning tunneling microscopy, and a plethora of new developments in analytical chemistry and electrochemical te- niques, permits the detailed characterization of atomic distribution, before, during, and after a reaction takes place, giving unpre- dented information about the status of the catalyst during the re- tion, and most importantly the time evolution of the exposed ca- lytic surfaces at the atomistic level. These techniques are c- plemented by the use of ab initio methods which do not require input from experimental information, and are based on numerical solutions of the time-independent Schrodinger equation including electron-electron and electron-atom interactions. These fir- principles computational methods have reached a degree of - turity such that their use to provide guidelines for interpretation of experiments and for materials design has become a routine practice in academic and industrial communities.

Electrocatalysts are the heart of power devices where electricity is produced via conversion of chemical into electrical energy. - pressive advances in surface science techniques and in first pr- ciples computational design are providing new avenues for signi- cant improvement of the overall efficiencies of such power dev- es, especially because of an increase in the understanding of el- trocatalytic materials and processes. For example, the devel- ment of high resolution instrumentation including various electron and ion-scattering and in-situ synchrotron spectroscopies, elect- chemical scanning tunneling microscopy, and a plethora of new developments in analytical chemistry and electrochemical te- niques, permits the detailed characterization of atomic distribution, before, during, and after a reaction takes place, giving unpre- dented information about the status of the catalyst during the re- tion, and most importantly the time evolution of the exposed ca- lytic surfaces at the atomistic level. These techniques are c- plemented by the use of ab initio methods which do not require input from experimental information, and are based on numerical solutions of the time-independent Schrodinger equation including electron-electron and electron-atom interactions. These fir- principles computational methods have reached a degree of - turity such that their use to provide guidelines for interpretation of experiments and for materials design has become a routine practice in academic and industrial communities.

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. This book was written for a senior undergraduate or a first year graduate student course in chemical engineering. Most of the examples in this book were done in Maple 10. However, the codes should run in the most recent version of Maple. We strongly encourage the readers to use the classic worksheet (*. mws) option in Maple as we believe it is more user-friendly and robust. In chapter one you will find an introduction to Maple which includes simple basics as a convenience for the reader such as plotting, solving linear and nonlinear equations, Laplace transformations, matrix operations, 'do loop,' and 'while loop. ' Chapter two presents linear ordinary differential equations in section 1 to include homogeneous and nonhomogeneous ODEs, solving systems of ODEs using the matrix exponential and Laplace transform method. In section two of chapter two, nonlinear ordinary differential equations are presented and include simultaneous series reactions, solving nonlinear ODEs with Maple's 'dsolve' command, stop conditions, differential algebraic equations, and steady state solutions. Chapter three addresses boundary value problems.