Scaling of Differential Equations: "Analysis of the Fourth Kind"


  • Paul J. Sides Carnegie Mellon University


An algebraic approach to scaling differential equations is presented.  The method allows deduction of common dimensionless groups and other useful relationships by applying simple rules to differential equations.  Called "All natural scaling", the process develops insight into problems.  The hypothesis of this contribution is that the student entering graduate school will find this approach to scaling equations useful; the student can derive dimensionless groups encountered in chemical engineering and thereby witness the generation of these groups.

Author Biography

Paul J. Sides, Carnegie Mellon University

Paul J. Sides is currently Professor of Chemical Engineering at Carnegie Mellon University. He received his BSChE from the University of Utah in 1973 and his PhD in Chemical Engineering from the University of California at Berkeley in 1981. He joined the faculty of the Department of Chemical Engineering at Carnegie Mellon in 1981. He has published articles in electrochemical engineering, growth of advanced materials, and data storage technology.