Basic Principles and Calculations in Chemical Engineering, 9th Edition

Appendix LSolution of Sets of Equations

This appendix contains a brief summary of methods of solving linear and nonlinear equations. It is only a summary; for details consult one of the numerous texts on numerical analysis that can be found in any library or one of the tutorials on the Internet.

L.1 Independent Linear Equations

1. What does the term linear mean?

The ease and accuracy of solving sets of equations often depends on whether the equations are linear or nonlinear. An equation is linear if it has (a) the property of proportionality and (b) the property of superposition.

Let L be a linear operator that causes a transformation of a variable x to another variable y. Then, for linearity:

1. Proportionality occurs

   y=L(kx)=kL(x)

2. Superposition ...