Books and Papers
New Edition, 2012
Web Book on Numerical Analysis
Introduction to Chemical Engineering Computing (2012) teaches you how to solve chemical engineering problems using the programs Excel, MATLAB, AspenPlus, and Comsol Multiphysics. The emphasis is on showing how to show your solution is valid rather than on the numerical analysis. A new version emphasizing AspenPlus 8 will be available in April, 2014.
For those more mathematically inclinded, error bounds and variational principles are desribed in Method of Weighted Residuals and Variational Principles, published in 1972 and republished as a SIAM Classic in 2014. New problems are available on the website.
See also Nonliinear Analysis in Chemical Engineering is a 2003 reprint in paperback of the 1980 McGraw-Hill book. This book describes many of the numerical methods used in current software to solve algebraic equations, ordinary differential equations as initial value problems and boundary value problems, and partial differential equations.
The WebBook on Numerical Analysis provides details about numerical analysis, available on this web site.